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800 | A cohomology for vector valued differential forms | math.DG | A rather simple natural outer derivation of the graded Lie algebra of all
vector valued differential forms with the Fr\"olicher-Nijenhuis bracket turns
out to be a differential and gives rise to a cohomology of the manifold, which
is functorial under local diffeomorphisms. This cohomology is determined as the
direct pr... | math |
801 | Nonunique tangent maps at isolated singularities of harmonic maps | math.DG | Shoen and Uhlenbeck showed that ``tangent maps'' can be defined at singular
points of energy minimizing maps. Unfortunately these are not unique, even for
generic boundary conditions. Examples are discussed which have isolated
singularities with a continuum of distinct tangent maps. | math |
802 | Graded derivations of the algebra of differential forms associated with a connection | math.DG | In the main part of this paper a connection is just a fiber projection onto a
(not necessarily integrable) distribution or sub vector bundle of the tangent
bundle. Here curvature is computed via the Froelicher-Nijenhuis bracket, and it
is complemented by cocurvature and the Bianchi identity still holds. In this
situati... | math |
803 | The action of the diffeomorphism group on the space of immersions | math.DG | We study the action of the diffeomorphism group $\Diff(M)$ on the space of
proper immersions $\Imm_{\text{prop}}(M,N)$ by composition from the right. We
show that smooth transversal slices exist through each orbit, that the quotient
space is Hausdorff and is stratified into smooth manifolds, one for each
conjugacy clas... | math |
804 | The relation between systems and associated bundles | math.DG | It is shown that a strong system of vector fields on a fiber bundle in the
sense of [Modugno, M. Systems of connections and invariant lagrangians. In:
Differential geometric methods in theoretical physics, Proc. 15th Int. Conf.,
DGM, Clausthal/FRG 1986, 518-534 World Scientific Publishing Co. (1987)] is
induced from a ... | math |
805 | Commutators of flows and fields | math.DG | The well known formula $[X,Y]=\tfrac12\tfrac{\partial^2}{\partial t^2}|_0
(\Fl^Y_{-t}\o\Fl^X_{-t}\o\Fl^Y_t\o\Fl^X_t)$ for vector fields $X$, $Y$ is
generalized to arbitrary bracket expressions and arbitrary curves of local
diffeomorphisms. | math |
806 | Geodesics on spaces of almost hermitian structures | math.DG | A natural metric on the space of all almost hermitian structures on a given
manifold is investigated. | math |
807 | One cannot hear the shape of a drum | math.DG | We use an extension of Sunada's theorem to construct a nonisometric pair of
isospectral simply connected domains in the Euclidean plane, thus answering
negatively Kac's question, ``can one hear the shape of a drum?'' In order to
construct simply connected examples, we exploit the observation that an
orbifold whose unde... | math |
808 | Characteristic classes for $G$-structures | math.DG | Let $G\subset GL(V)$ be a linear Lie group with Lie algebra $\frak g$ and let
$A(\frak g)^G$ be the subalgebra of $G$-invariant elements of the associative
supercommutative algebra $A(\frak g)= S(\frak g^*)\otimes \La(V^*)$. To any
$G$-structure $\pi:P\to M$ with a connection $\omega$ we associate a
homomorphism $\mu_\... | math |
809 | Adding handles to the helicoid | math.DG | There exist two new embedded minimal surfaces, asymptotic to the helicoid.
One is periodic, with quotient (by orientation-preserving translations) of
genus one. The other is nonperiodic of genus one. | math |
810 | Differential geometry of $\frak g$-manifolds | math.DG | An action of a Lie algebra $\frak g$ on a manifold $M$ is just a Lie algebra
homomorphism $\zeta:\frak g\to \frak X(M)$. We define orbits for such an
action. In general the space of orbits $M/\frak g$ is not a manifold and even
has a bad topology. Nevertheless for a $\frak g$-manifold with equidimensional
orbits we tre... | math |
811 | A theory of characteristic currents associated with a singular connection | math.DG | This note announces a general construction of characteristic currents for
singular connections on a vector bundle. It develops, in particular, a
Chern-Weil-Simons theory for smooth bundle maps $\alpha : E \rightarrow F$
which, for smooth connections on $E$ and $F$, establishes formulas of the type
$$ \phi \ = \ \text{\... | math |
812 | On the Asymptotic Behavior of Counting Functions Associated to Degenerating Hyperbolic Riemann Surfaces | math.DG | We develop an asymptotic expansion of the spectral measures on a degenerating
family of hyperbolic Riemann surfaces of finite volume. As an application of
our results, we study the asymptotic behavior of weighted counting functions,
which, if $M$ is compact, is defined for $w \geq 0$ and $T > 0$ by $$N_{M,w}(T)
= \sum\... | math |
813 | Differential geometry of Cartan connections | math.DG | For a more general notion of Cartan connection we define characteristic
classes, we investigate their relation to usual characteristic classes. | math |
814 | A New Construction of Isospectral Riemannian Nilmanifolds with Examples | math.DG | We present a new construction for obtaining pairs of higher-step isospectral
Riemannian nilmanifolds and compare several resulting new examples. In
particular, we present new examples of manifolds that are isospectral on
functions, but not isospectral on one-forms. | math |
815 | Geometric Zeta Functions, $L^2$-Theory, and Compact Shimura Manifolds | math.DG | We define geometric zeta functions for locally symmetric spaces as
generalizations of the zeta functions of Ruelle and Selberg. As a special value
at zero we obtain the Reidemeister torsion of the manifold. For hermitian
spaces these zeta functions have as special value the quotient of the
holomorphic torsion of Ray an... | math |
816 | Geodesic Conjugacy in two-step nilmanifolds | math.DG | Two Riemannian manifolds are said to have $C^k$-conjugate geodesic flows if
there exist an $C^k$ diffeomorphism between their unit tangent bundles which
intertwines the geodesic flows. We obtain a number of rigidity results for the
geodesic flows on compact 2-step Riemannian nilmanifolds: For generic 2-step
nilmanifold... | math |
817 | Filling-invariants at infinity for manifolds of nonpositive curvature | math.DG | In this paper we construct and study isoperimetric functions at infinity for
Hadamard manifolds. These quasi-isometry invariants give a measure of the
spread of geodesics in such a manifold. | math |
818 | Arithmeticity, Discreteness and Volume | math.DG | We give an arithmetic criterion which is sufficient to imply the discreteness
of various two-generator subgroups of $PSL(2,{\bold C})$. We then examine
certain two-generator groups which arise as extremals in various geometric
problems in the theory of Kleinian groups, in particular those encountered in
efforts to dete... | math |
819 | On the Margulis constant for Kleinian groups, I curvature | math.DG | The Margulis constant for Kleinian groups is the smallest constant $c$ such
that for each discrete group $G$ and each point $x$ in the upper half space
${\bold H}^3$, the group generated by the elements in $G$ which move $x$ less
than distance c is elementary. We take a first step towards determining this
constant by p... | math |
820 | A note on Carnot geodesics in nilpotent Lie groups | math.DG | We show that strictly abnormal geodesics arise in graded nilpotent Lie
groups. We construct such a group, for which some Carnot geodesics are strictly
abnormal; in fact, they are not normal in any subgroup. In the step-2 case we
also prove that these geodesics are always smooth. Our main technique is based
on the equat... | math |
821 | Complete embedded minimal surfaces of finite total curvature | math.DG | We survey what is known about minimal surfaces in $\bold R^3 $ that are
complete, embedded, and have finite total curvature. The only classically known
examples of such surfaces were the plane and the catenoid. The discovery by
Costa, early in the last decade, of a new example that proved to be embedded
sparked a great... | math |
822 | Grafting, harmonic maps, and projective structures on surfaces | math.DG | Grafting is a surgery on Riemann surfaces introduced by Thurston which
connects hyperbolic geometry and the theory of projective structures on
surfaces. We will discuss the space of projective structures in terms of the
Thurston's geometric parametrization given by grafting. From this approach we
will prove that on any... | math |
823 | The Marked Length Spectrum Versus the Laplace Spectrum on Forms on Riemannian Nilmanifolds | math.DG | The subject of this paper is the relationship among the marked length
spectrum, the length spectrum, the Laplace spectrum on functions, and the
Laplace spectrum on forms on Riemannian nilmanifolds. In particular, we show
that for a large class of three-step nilmanifolds, if a pair of nilmanifolds in
this class has the ... | math |
824 | Hodge theory in the Sobolev topology for the de Rham complex | math.DG | The authors study the Hodge theory of the exterior differential operator $d$
acting on $q$-forms on a smoothly bounded domain in $\RR^{N+1}$, and on the
half space $\rnp$. The novelty is that the topology used is not an $L^2$
topology but a Sobolev topology. This strikingly alters the problem as compared
to the classic... | math |
825 | Homogeneous Special Geometry | math.DG | Motivated by the physical concept of special geometry two mathematical
constructions are studied, which relate real hypersurfaces to tube domains and
complex Lagrangean cones respectively. Me\-thods are developed for the
classification of homogeneous Riemannian hypersurfaces and for the
classification of linear transit... | math |
826 | Quasiconformality and geometrical finiteness in Carnot--Carathéodory and negatively curved spaces | math.DG | The paper sketches a recent progress and formulates several open problems in
studying equivariant quasiconformal and quasisymmetric homeomorphisms in
negatively curved spaces as well as geometry and topology of noncompact
geometrically finite negatively curved manifolds and their boundaries at
infinity having Carnot--C... | math |
827 | An estimate for the Gauss curvature of minimal surfaces in $\mathbb R^m$ whose Gauss map omits a set of hyperplanes | math.DG | We give an estimate of the Gauss curvature for minimal surfaces in ${\mathbb
R}^m$ whose Gauss map omits more than $m(m+1)/2$ hyperplanes in ${\mathbb
P}^{m-1}({\mathbb C})$. | math |
828 | The Singly Periodic Genus-One Helicoid | math.DG | We prove the existence of a complete, embedded, singly periodic minimal
surface, whose quotient by vertical translations has genus one and two ends.
The existence of this surface was announced in our paper in {\it Bulletin of
the AMS}, 29(1):77--84, 1993. Its ends in the quotient are asymptotic to one
full turn of the ... | math |
829 | Asymptotic geometry and conformal types of Carnot--Carathéodory spaces | math.DG | An intrinsic definition in terms of conformal capacity is proposed for the
conformal type of a Carnot--Carath\'eodory space (parabolic or hyperbolic).
Geometric criteria of conformal type are presented. They are closely related to
the asymptotic geometry of the space at infinity and expressed in terms of the
isoperimet... | math |
830 | Mixing Mathematics and Materials | math.DG | Recent uses of differential geometry in materials science are reviewed here,
in particular the September issue of the Phil. Trans. Royal Soc., entitled
``Curvature and chemical Structure.'' | math |
831 | The Jacobi flow | math.DG | The geodesic flow on the tangent bundle is the flow of a certain vector field
which is called the spray $S:TM\to TTM$. The flow lines of the vector field
$\ka_{TM}\o TS:TTM\to TTTM$ project to the Jacobi fields on $TM$. This could be
called the Jacobi flow. | math |
832 | Flattening and subanalytic sets in rigid analytic geometry | math.DG | Let K be an algebraically closed field endowed with a complete
non-archimedean norm with valuation ring R. Let f:Y -> X be a map of K-affinoid
varieties. In this paper we study the analytic structure of the image f(Y) in
X; such an image is a typical example of a subanalytic set. We show that the
subanalytic sets are p... | math |
833 | Verdier stratifications and [wf]-stratification in o-minimal structures | math.DG | We prove the existence of Verdier stratifications for sets definable in any
o-minimal structure on (R, +, .). It is also shown that the Verdier condition
(w) implies the Whitney condition (b) in o-minimal structures on (R, +, .). As
a consequence the Whitney Stratification Theorem holds. The existence of
(wf)-stratific... | math |
834 | On the bifurcation sets of functions definable in o-minimal structures | math.DG | Let g:X -> Y be a smooth (i.e. C^\infty differentiable) map between two
smooth manifolds. In analogy with the case of complex polynomial functions, we
say that y_0 in Y is a typical value of g if there exists an open neighbourhood
U of y_0 in Y, such that the restriction g:g^{-1}(U) -> U is a C^\infty trivial
fibration... | math |
835 | Closure of rigid semianalytic sets | math.DG | Let K be an algebraically closed field of characteristic zero, endowed with a
complete nonarchimedean norm. Let X be a K-rigid analytic variety and \Sigma a
semianalytic subset of X. Then the closure of \Sigma in X with respect to the
canonical topology is again semianalytic. The proof uses Embedded Resolution of
Singu... | math |
836 | Motion by weighted mean curvature is affine invariant | math.DG | Suppose curves are moving by curvature in a plane, but one embeds the plane
in $R^3$ and looks at the plane from an angle. Then circles shrinking to a
round point would appear to be ellipses shrinking to an ``elliptical point,''
and the surface energy would appear to be anisotropic as would the mobility.
The result of ... | math |
837 | Vertex theorems for capillary drops on support planes | math.DG | We consider a capillary drop that contacts several planar bounding walls so
as to produce singularities (vertices) in the boundary of its free surface. It
is shown under various conditions that when the number of vertices is less than
or equal to three, then the free surface must be a portion of a sphere. These
results... | math |
838 | Ward's solitions | math.DG | Using the `Riemann Problem with zeros' method, Ward has constructed exact
solutions to a (2+1)-dimensional integrable Chiral Model, which exhibit
solitons with nontrivial scattering. We give a correspondence between what we
conjecture to be all pure soliton solutions and certain holomorphic vector
bundles on a compact ... | math |
839 | Functions on space curves | math.DG | We classify simple singularities of functions on space curves. We show that
their bifurcation sets have properties very similar to those of functions on
smooth manifolds and complete intersections [1,2]: the k(pi, 1)-theorem for the
bifurcations diagram of functions is true, and both this diagram and the
discriminant a... | math |
840 | Embedded minimal ends asymptotic to the helicoid | math.DG | The ends of a complete embedded minimal surface of {\em finite total
curvature} are well understood (every such end is asymptotic to a catenoid or
to a plane). We give a similar characterization for a large class of ends of
{\em infinite total curvature}, showing that each such end is asymptotic to a
helicoid. The resu... | math |
841 | Generalization of the Chekanov theorem: diameters of immersed manifolds and wave fronts | math.DG | The Chekanov theorem generalizes the classic Lyusternik-Shnirel'man and Morse
theorems concerning critical points of a smooth function on a closed manifold.
A Legendrian submanifold \Lambda of space of 1-jets of the functions on a
manifold M defines a multi-valued function whose graph is the projection of
\Lambda in J^... | math |
842 | Variational problems for Riemannian functionals and arithmetic groups | math.DG | In this paper we introduce a new approach to variational problems on the
space Riem(M^n) of Riemannian structures (i.e. isometry classes of Riemannan
metrics) on any fixed compact manifold M^n of dimension n >= 5. This approach
often enables one to replace the considered variational problem on Riem(M^n)
(or on some sub... | math |
843 | Regular infinite dimensional Lie groups | math.DG | Regular Lie groups are infinite dimensional Lie groups with the property that
smooth curves in the Lie algebra integrate to smooth curves in the group in a
smooth way (an `evolution operator' exists). Up to now all known smooth Lie
groups are regular. We show in this paper that regular Lie groups allow to push
surprisi... | math |
844 | The Weierstrass representation of spheres in $R^3$, the Willmore numbers, and soliton spheres | math.DG | The Weierstrass representation for spheres in $\R^3$ and, in particular,
effective construction of immersions from data of spectral theory origin is
discussed. These data are related to Dirac operators on a plane and on an
infinite cylinder and these operators are just representations of Dirac
operators acting in spino... | math |
845 | No slices on the space of generalized connections | math.DG | On a fiber bundle without structure group the action of the gauge group (the
group of all fiber respecting diffeomorphisms) on the space of (generalized)
connections is shown not to admit slices. | math |
846 | Poisson structures on double Lie groups | math.DG | Lie bialgebra structures are reviewed and investigated in terms of the double
Lie algebra, of Manin- and Gau{\ss}-decompositions. The standard R-matrix in a
Manin decomposition then gives rise to several Poisson structures on the
correponding double group, which is investigated in great detail. | math |
847 | Lifting smooth curves over invariants for representations of compact Lie groups | math.DG | We show that one can lift locally real analytic curves from the orbit space
of a compact Lie group representation, and that one can lift smooth curves even
globally, but under an assumption. | math |
848 | A tangent bundle on diffeological spaces | math.DG | We define a subcategory of the category of diffeological spaces, which
contains smooth manifolds, the diffeomorphism subgroups and its coadjoint
orbits. In these spaces we construct a tangent bundle, vector fields and a de
Rham cohomology. | math |
849 | Hofer's diameter and Lagrangian intersections | math.DG | We prove that the group of Hamiltonian diffeomorphisms of the 2-sphere has
infinite diameter with respect to Hofer's metric. Our approach is based on the
theory of Lagrangian intersections. | math |
850 | Curvature of the Virasoro-Bott group | math.DG | We consider a natural Riemannian metric on the infinite dimensional manifold
of all embeddings from a manifold into a Riemannian manifold, and derive its
geodesic equation in the case $\Emb(\Bbb R,\Bbb R)$ which turns out to be
Burgers' equation. Then we derive the geodesic equation, the curvature, and the
Jacobi equat... | math |
851 | On the cohomology of sl(m+1,R) acting on differential operators and sl(m+1,R)-equivariant symbol | math.DG | One computes the cohomology of the projective embedding of sl(m+1,R) acting
on the differential operators on densities on R^m of various weights. This
cohomology is non vanishing only for some special critical values of the
weights. This allows us first to explain some strange feature pointed out by
Gargoubi in his cla... | math |
852 | On the case of Goryachev-Chaplygin and new examples of integrable conservative systems on S^2 | math.DG | The aim of this paper is to describe a class of conservative systems on $S^2$
possessing an integral cubic in momenta. We prove that this class of systems
consists off the case of Goryachev-Chaplygin, the one-parameter family of
systems which has been found by the author in the previous paper
(dg-ga/9711005) and a new ... | math |
853 | Metrics of constant curvature 1 with three conical singularities on 2-sphere | math.DG | A necessary and sufficient condition for the existence and uniqueness of a
conformal metric on 2-sphere of constant curvature 1 and with three conical
singularities of prescribed order is given. | math |
854 | The outer derivation of a complex Poisson manifold | math.DG | We introduce a canonical outer vector field on a Poisson manifold, also due
independently to A. Weinstein. We view it as a global section of the sheaf of
Poisson vector fields modulo the subsheaf of hamiltonian vector fields. We
study this outer derivation mostly in the case of holomorphic Poisson
manifolds. | math |
855 | Cartan Spinor Bundles on Manifolds | math.DG | The aim of this paper is the construction of spinor bundles of Cartan type
over certain non-orientable manifolds. | math |
856 | Holomorphic spinors and the Dirac equation | math.DG | A closed spin K\"ahler manifold of positive scalar curvature with smallest
possible first eigenvalue of the Dirac operator is characterized by holomorphic
spinors. It is shown that on any spin K\"ahler-Einstein manifold each
holomorphic spinor is a finite sum of eigenspinors of the square of the Dirac
operator. Vanishi... | math |
857 | Gluing theorems for anti-self-dual metrics | math.DG | In this paper we announce a gluing theorem for conformal structures with
anti-self-dual (ASD) Weyl tensor that applies in geometrical situations that
are more general than those considered by previous authors. By adapting a
method proposed by Floer, sufficient conditions are given for the existence of
ASD conformal str... | math |
858 | A four dimensional example of Ricci-flat metric admitting almost-Kähler non-Káhler structure | math.DG | We construct an example of Ricci-flat almost-K\"ahler non-K\"ahler structure
in four dimensions. | math |
859 | Mathai-Quillen forms and Lefschetz theory | math.DG | Mathai-Quillen forms are used to give an integral formula for the Lefschetz
number of a smooth map of a closed manifold. Applied to the identity map, this
formula reduces to the Chern-Gauss-Bonnet theorem. The formula is computed
explicitly for constant curvature metrics. There is in fact a one-parameter
family of inte... | math |
860 | The loop derivative as a curvature | math.DG | Recently, a set of tools has been developed with the purpose of the study of
Quantum Gravity. Until now, there have been very few attempts to put these
tools into a rigorous mathematical framework. This is the case, for example, of
the so called path bundle of a manifold. It is well known that this topological
principa... | math |
861 | Higher analytic torsion of sphere bundles and continuous cohomology of $Diff(S^{2n-1})$ | math.DG | Using the higher analytic torsion form of Bismut and Lott we construct a
characteristic class for smooth sphere bundles. We calculate this class in the
case where the sphere bundle comes from a complex vector bundle. Related to
these characteristic classes we define nontrivial continuous group cohomology
classes of the... | math |
862 | Symplectic reduction and a weighted multiplicity formula for twisted Spin$^c$-Dirac operators | math.DG | We extend our earlier work in [TZ1], where an analytic approach to the
Guillemin-Sternberg conjecture [GS] was developed, to cases where the
Spin$^c$-complex under consideration is allowed to be further twisted by
certain natural exterior power bundles. The main result is a weighted
quantization formula in the presence... | math |
863 | Singularities and bifurcations of 3-dimensional Poisson structure | math.DG | We give a normal form for families of 3-dimensional Poisson structures. This
allows us to classify singularities with nonzero 1-jet and typical
bifurcations. The Appendix contains corollaries on classification of families
of integrable 1-forms on $R^3 | math |
864 | Orthogonal nets and Clifford algebras | math.DG | A Clifford algebra model for M"obius geometry is presented. The notion of
Ribaucour pairs of orthogonal systems in arbitrary dimensions is introduced,
and the structure equations for adapted frames are derived. These equations are
discretized and the geometry of the occuring discrete nets and sphere
congruences is disc... | math |
865 | Torus Curves With Vanishing Curvature | math.DG | Let T be the standard torus of revolution in R^3 with radii b and 1, 0<b<1.
Let \alpha be a (p,q) torus curve on T. We show that there are points of zero
curvature on \alpha for only one value of the variable radius of T,
b=p^2/(p^2+q^2). The curve \alpha has non-vanishing curvature for all other
values of b. Moreover,... | math |
866 | On Gromov's theory of rigid transformation groups: A dual approach | math.DG | Geometric problems are usually formulated by means of (exterior) differential
systems. In this theory, one enriches the system by adding algebraic and
differential constraints, and then looks for regular solutions.
Here we adopt a dual approach, which consists to enrich a plane field, as
this is often practised in co... | math |
867 | Parallel spinors and holonomy groups on pseudo-Riemannian spinmanifolds | math.DG | We describe the possible holonomy groups of simply connected irreducible
non-locally symmetric pseudo-Riemannian spin manifolds which admit parallel
spinors. | math |
868 | Lagrangian two-spheres can be symplectically knotted | math.DG | This paper shows that there are symplectic four-manifolds M with the
following property: a single isotopy class of smooth embedded two-spheres in M
contains infinitely many Lagrangian submanifolds, no two of which are isotopic
as Lagrangian submanifolds. The examples are constructed using a special class
of symplectic ... | math |
869 | Symplectic automorphisms of T^*S^2 | math.DG | Let M be the cotangent bundle of S^2, with the standard symplectic structure.
By adapting an argument of Gromov we determine the weak homotopy type of the
group S of those symplectic automorphisms of M which are trivial at infinity.
It turns out that S is weakly homotopy equivalent to \Z. \pi_0(S) is generated
by the c... | math |
870 | On the group of symplectic automorphisms of $\C P^m \times \C P^n$ | math.DG | Let M be the product of \C P^m and \C P^n, with the standard integral
symplectic form. We prove that the inclusion map from the group of symplectic
automorphisms of M to its diffeomorphism group is not surjective on homotopy
groups. More precisely, it is not surjective on \pi_j for all odd j \leq
\max\{2m-1,2n-1\}. Thi... | math |
871 | On the Noncommutative Geometry of the Endomorphism Algebra of a Vector Bundle | math.DG | In this letter we investigate some aspects of the noncommutative differential
geometry based on derivations of the algebra of endomorphisms of an oriented
complex hermitian vector bundle. We relate it, in a natural way, to the
geometry of the underlying principal bundle and compute the cohomology of its
complex of nonc... | math |
872 | Twistor spinors on Lorentzian symmetric spaces | math.DG | We solve the twistor equation on all indecomposable Lorentzian symmetric
spaces explicity. | math |
873 | Lorentzian twistor spinors and CR-geometry | math.DG | We prove that there exist global solutions of the twistor equation on the
Fefferman spaces of strictly pseudoconvex spin manifolds of arbitrary dimension
and we study their properties. | math |
874 | Dolbeault Cohomology of compact Nilmanifolds | math.DG | Let $M= G/\Gamma$ be a compact nilmanifold endowed with an invariant complex
structure. We prove that, on an open set of any connected component of the
moduli space ${\cal C} ({\frak g})$ of invariant complex structures on $M$, the
Dolbeault cohomology of $M$ is isomorphic to the one of the differential
bigraded algebr... | math |
875 | On the Cappell-Lee-Miller glueing theorem | math.DG | We formulate a more conceptual interpretation of the Cappell-Lee-Miller
glueing/splitting theorem using the new language of asymptotic maps and
asymptotic exactness. Additionally, we present an asymptotic description of the
Mayer-Vietoris sequence naturally associated to the Cech cohomology of the
sheaf of local soluti... | math |
876 | Fukaya Floer homology of $Σ\times S^1$ and applications | math.DG | We determine the Fukaya Floer homology of the three-manifold which is the
product of a Riemann surface of genus $g\geq 1$ times the circle. This sets up
the groundwork for finding the structure of the Donaldson invariants of
four-manifolds not of simple type in the future. We give the following
applications: 1) We show... | math |
877 | Rigidity of area minimizing tori in 3-manifolds of nonnegative scalar curvature | math.DG | The following version of a conjecture of Fischer-Colbrie and Schoen is
proved: If M is a complete Riemannian 3-manifold with nonnegative scalar
curvature which contains a two-sided torus S which is of least area in its
isotopy class then M is flat. This follows from a local version derived in the
paper. | math |
878 | Signatures and Higher Signatures of $S^1$-Quotients | math.DG | We define and study the signature, A-hat genus and higher signatures of the
quotient space of an $S^1$-action on a closed oriented manifold. We give
applications to questions of positive scalar curvature and to an Equivariant
Novikov Conjecture. | math |
879 | The Gaussian Measure On Algebraic Varieties | math.DG | We prove that the ring $\Aff{\R}{M}$ of all polynomials defined on a real
algebraic variety $M\subset\R^n$ is dense in the Hilbert space
$L^2(M,e^{-|x|^2}\de\mu)$, where $\de\mu$ denotes the volume form of $M$ and
$\de\nu=e^{-|x|^2}\de\mu$ the Gaussian measure on $M$. | math |
880 | Chern classes of modular varieties | math.DG | Let X be a Hermitian locally symmetric space. We prove that every Chern class
of X has a canonical lift to the cohomology of the Baily- Borel-Satake
compactification X* of X and that the resulting Chern numbers satisfy the
Hirzebruch proportionality formula with respect to the compact dual X^ of X.
The same result hold... | math |
881 | Equivariant Cohomology and Wall Crossing Formulas in Seiberg-Witten Theory | math.DG | We use localization formulas in the theory of equivariant cohomology to
rederive the wall crossing formulas of Li-Liu and Okonek-Teleman for
Seiberg-Witten invariants. | math |
882 | Hodge theory and cohomology with compact supports | math.DG | This paper constructs a Hodge theory of noncompact topologically tame
manifolds $M$. The main result is an isomorphism between the de Rham cohomology
with compact supports of $M$ and the kernel of the Hodge--Witten--Bismut
Laplacian $\lap_\mu$ associated to a measure $d\mu$ which has sufficiently
rapid growth at infini... | math |
883 | Stationary Veselov-Novikov equation and isothermally asymptotic surfaces in projective differential geometry | math.DG | It is demonstrated that the stationary Veselov-Novikov (VN) and the
stationary modified Veselov-Novikov (mVN) equations describe one and the same
class of surfaces in projective differential geometry: the so-called
isothermally asymptotic surfaces, examples of which include arbitrary quadrics
and cubics, quartics of Ku... | math |
884 | Surfaces with flat normal bundle: an explicit construction | math.DG | An explicit construction of surfaces with flat normal bundle in the Euclidean
space (unit hypersphere) in terms of solutions of certain linear system is
proposed. In the case of 3-space our formulae can be viewed as the direct Lie
sphere analog of the generalized Weierstrass representation of surfaces in
conformal geom... | math |
885 | Invariant local twistor calculus for quaternionic structures and related geometries | math.DG | New universal invariant operators are introduced in a class of geometries
which include the quaternionic structures and their generalisations as well as
4-dimensional conformal (spin) geometries. It is shown that, in a broad sense,
all invariants and invariant operators arise from these universal operators and
that the... | math |
886 | A traditional dealing with a semi-classical limit and Hopf theorem | math.DG | This paper deals with a semi-classical limit (Theorem 1) by using traditional
mathematical methods, and shows a Hopf theorem as a corollary. A formal
discussion of it may be found in [7]. | math |
887 | Invariant Forms and Automorphisms of Locally Homogeneous Multisymplectic Manifolds | math.DG | It is shown that the geometry of locally homogeneous multisymplectic
manifolds (that is, smooth manifolds equipped with a closed nondegenerate form
of degree > 1, which is locally homogeneous of degree k with respect to a local
Euler field) is characterized by their automorphisms. Thus, locally homogeneous
multisymplec... | math |
888 | Eta invariants of Dirac operators on Circle bundles over Riemann surfaces and virtual dimensions of finite energy Seiberg-Witten moduli spaces | math.DG | We compute eta invariants of various Dirac type operators on circle bundles
over Riemann surfaces via two approaches: an adiabatic approach based on the
results of Bismut-Cheeger-Dai and a direct elementary one. These results,
coupled with some delicate spectral flow computations are then used to
determine the virtual ... | math |
889 | Equifocal families in symmetric spaces of compact type | math.DG | An equifocal submanifold M of a symmetric space N of compact type induces a
foliation with singular leaves on N. In this paper we will show how to
reconstruct the equifocal foliation starting from one of the singular leaves,
the so-called focal manifolds. To be more concrete: The equifocal submanifold
is equal to a par... | math |
890 | L2-torsion of hyperbolic manifolds | math.DG | The L^2-torsion is an invariant defined for compact L^2-acyclic manifolds of
determinant class, for example odd dimensional hyperbolic manifolds. It was
introduced by John Lott and Varghese Mathai and computed for hyperbolic
manifolds in low dimensions.
In this paper we show that the L^2-torsion of hyperbolic manifol... | math |
891 | Semiintegrable almost Grassmann structures | math.DG | In the present paper we study locally semiflat (we also call them
semiintegrable) almost Grassmann structures. We establish necessary and
sufficient conditions for an almost Grassmann structure to be alpha- or
beta-semiintegrable. These conditions are expressed in terms of the fundamental
tensors of almost Grassmann st... | math |
892 | Conformal and Grassmann structures | math.DG | The main results on the theory of conformal and almost Grassmann structures
are presented. The common properties of these structures and also the
differences between them are outlined. In particular, the structure groups of
these structures and their differential prolongations are found. A complete
system of geometric ... | math |
893 | On the theory of almost Grassmann structures | math.DG | The differential geometry of almost Grassmann structures defined on a
differentiable manifold of dimension n = pq by a fibration of Segre cones SC
(p, q) is studied. The peculiarities in the structure of almost Grassmann
structures for the cases p=q=2; p = 2, q > 2 (or p > 2, q = 2), and p > 2, q >
2 are clarified. The... | math |
894 | A conformal differential invariant and the conformal rigidity of hypersurfaces | math.DG | For a hypersurface V of a conformal space, we introduce a conformal
differential invariant I = h^2/g, where g and h are the first and the second
fundamental forms of V connected by the apolarity condition. This invariant is
called the conformal quadratic element of V. The solution of the problem of
conformal rigidity i... | math |
895 | Singular points of lightlike hypersurfaces of the de Sitter space | math.DG | The authors study singular points of lightlike hypersurfaces of the de Sitter
space S^{n+1}_1 and the geometry of hypersurfaces and use them for construction
of an invariant normalization and an invariant affine connection of lightlike
hypersurfaces. | math |
896 | Upper bounds for the first eigenvalue of the Dirac operator on surfaces | math.DG | In this paper we will prove new extrinsic upper bounds for the eigenvalues of
the Dirac operator on an isometrically immersed surface $M^2 \hookrightarrow
{\Bbb R}^3$ as well as intrinsic bounds for 2-dimensional compact manifolds of
genus zero and genus one. Moreover, we compare the different estimates of the
eigenval... | math |
897 | On geometry of hypersurfaces of a pseudoconformal space of Lorentzian signature | math.DG | There are three types of hypersurfaces in a pseudoconformal space C^n_1 of
Lorentzian signature: spacelike, timelike, and lightlike. These three types of
hypersurfaces are considered in parallel. Spacelike hypersurfaces are endowed
with a proper conformal structure, and timelike hypersurfaces are endowed with
a conform... | math |
898 | On a normalization of a Grassmann manifold | math.DG | On the Grassmann manifold G (m, n) of m-dimensional subspaces of an
n-dimensional projective space P^n, a certain supplementary construction called
the normalization is considered. By means of this normalization, one can
construct the structure of a Riemannian or semi-Riemannian manifold or an
affine connection on G(m,... | math |
899 | Teichmuller theory and handle addition for minimal surfaces | math.DG | We develop Teichmuller theoretical methods to construct new minimal surfaces
in $\BE^3$ by adding handles and planar ends to existing minimal surfaces in
$\BE^3$. We exhibit this method on an interesting class of minimal surfaces
which are likely to be embedded, and have a low degree Gau\ss map for their
genus; the (We... | math |
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