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Differential Geometry papers — page 6

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Sequences of Levy Transformations and Multi-Wroński Determinant Solutions of the Darboux System
Sequences of Levy transformations for the Darboux system of conjugates nets in multidimensions are studied. We show that after a suitable number of Levy transformations, with at least a Levy…
Q. P. Liu, Manuel MañasJul 21, 1997
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Remark About Heat Diffusion on Periodic Spaces
Let M be a complete Riemannian manifold with a free cocompact Zk-action. Let k(t,x,y) be the heat kernel on M. We compute the asymptotics of k(t,x,y) in the limit in which t goes to infinity and…
John LottJul 18, 1997
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Torsion and fibrations
We study the behaviour of analytic torsion under smooth fibrations. Namely, let F E f B be a smooth fiber bundle of connected closed oriented smooth manifolds and let V be a flat vector…
Wolfgang Lueck, Thomas Schick, Thomas ThielmannJul 10, 1997
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L2-torsion of hyperbolic manifolds of finite volume
Suppose M is a compact connected odd-dimensional manifold with boundary, whose interior M comes with a complete hyperbolic metric of finite volume. We will show that the L2-topological…
Wolfgang Lueck, Thomas SchickJul 10, 1997
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Dimension theory of arbitrary modules over finite von Neumann algebras and applications to L2-Betti numbers
We define for arbitrary modules over a finite von Neumann algebra a dimension taking values in [0,∞] which extends the classical notion of von Neumann dimension for finitely generated…
Wolfgang LueckJul 10, 1997
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On nodal sets for Dirac and Laplace operators
We prove that the nodal set (zero set) of a solution of a generalized Dirac equation on a Riemannian manifold has codimension 2 at least. If the underlying manifold is a surface, then the nodal set…
Christian BaerJul 10, 1997
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Zeta Functions, Determinants and Torsion for Open Manifolds
On an open manifold, the spaces of metrics or connections of bounded geometry, respectively, split into an uncountable number of components. We show that for a pair of metrics or connections,…
J. EichhornJul 10, 1997
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Linearization of Nambu Structures
We classify linear Nambu structures (which are generalized Poisson structures in Hamiltonian dynamics and which give rise to integrable differential forms and singular foliations), then give a…
Jean Paul Dufour, Nguyen Tien ZungJul 10, 1997
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Equivariant Higher Analytic Torsion and Equivariant Euler Characteristic
We show that J. Lott's equivariant higher analytic torsion for compact group actions depends only on the equivariant Euler characteristic.
U. BunkeJul 9, 1997
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Poisson Actions and Scattering Theory for Integrable Systems
Conservation laws, heirarchies, scattering theory and Bäcklund transformations are known to be the building blocks of integrable partial differential equations. We identify these as facets of a…
Chuu-Lian Terng, Karen UhlenbeckJul 7, 1997
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Almost Diameter Rigidity for the Cayley Plane
In this paper we give a generalisation of the Radius Rigidity theorem of F.Wilhelm. This is done by showing that if a Riemannian submersion of S15 with 7-dimensional fibres has at least one…
Akhil RanjanJul 7, 1997
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Multivector Fields and Connections. Setting Lagrangian Equations in Field Theories
The integrability of multivector fields in a differentiable manifold is studied. Then, given a jet bundle J1E E M, it is shown that integrable multivector fields in E are equivalent to…
A. Echeverria-Enriquez, M. C. Munoz-Lecanda, N. Roman-RoyJul 3, 1997
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Systolic freedom of orientable manifolds
In 1972, Marcel Berger defined a metric invariant that captures the `size' of k-dimensional homology of a Riemannian manifold. This invariant came to be called the k-dimensional SYSTOLE. He asked…
Ivan Babenko, Mikhail KatzJul 3, 1997
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Quaternionic Killing Spinors
In a previous article we proved a lower bound for the spectrum of the Dirac operator on quaternionic Kaehler manifolds. In the present article we study the limiting case, i. e. manifolds where the…
W. Kramer, U. Semmelmann, G. WeingartJun 27, 1997
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Harmonic Spinors for Twisted Dirac Operators
We show that for a suitable class of ``Dirac-like'' operators there holds a Gluing Theorem for connected sums. More precisely, if M1 and M2 are closed Riemannian manifolds of dimension…
Christian BaerJun 27, 1997
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Simple homotopy type of the Novikov complex and Lefschetz ζ-function of the gradient flow
Let f be a Morse map from a closed manifold to a circle. S.P.Novikov constructed an analog of the Morse complex for f. The Novikov complex is a chain complex defined over the ring of Laurent power…
A. PajitnovJun 26, 1997
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On the Flux Conjectures
The ``Flux conjecture'' for symplectic manifolds states that the group of Hamiltonian diffeomorphisms is C1-closed in the group of all symplectic diffeomorphisms. We prove the conjecture for…
Francois Lalonde, Dusa McDuff, Leonid PolterovichJun 26, 1997
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Seiberg-Witten Equations on Three-Manifolds with Euclidean Ends
We construct the Seiberg-Witten theory on 3-manifolds with Euclidean ends (connected sums of 3 and a compact manifold) with perturbations which approximate *dx3 at infinity, and describe the…
Yi-Jen LeeJun 24, 1997
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Circle-valued Morse theory and Reidemeister torsion
Let X be a closed manifold with zero Euler characteristic, and let f: X --> S1 be a circle-valued Morse function. We define an invariant I which counts closed orbits of the gradient of f, together…
Michael Hutchings, Yi-Jen LeeJun 24, 1997
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The universal cover of an affine three-manifold with holonomy of shrinkable dimension ≤ 2
An affine manifold is a manifold with an affine structure, i.e. a torsion-free flat affine connection. We show that the universal cover of a closed affine 3-manifold M with holonomy group of…
Suhyoung ChoiJun 23, 1997
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Quantization formula for singular reductions
In this note, we prove a quantization formula for singular reductions. The main result is obtained as a simple application of an extended quantization formula proved in [TZ2].
Youliang Tian, Weiping ZhangJun 18, 1997
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Relative equilibria at singular points of the moment map
We prove a criterion for stability of relative equilibria in symmetric Hamiltonian systems at singular points of the momentum map. This generalizes a theorem of G.W. Patrick. The method of the proof…
Eugene LermanJun 12, 1997
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Duality of subanalytic sets
We study the link between a compact hypersurface in ¶n+1 and the set of all its tangent planes. In this context, we identify ¶n+1 to the set of linear subspaces of codimension one by…
Francois PointetJun 10, 1997
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A frame bundle generalization of multisymplectic field theories
This paper presents a generalization of symplectic geometry to a principal bundle over the configuration space of a classical field. This bundle, the vertically adapted linear frame bundle, is…
J. K. LawsonJun 10, 1997
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On the homotopy invariance of L2 torsion for covering spaces
We prove the homotopy invariance of L2 torsion for covering spaces, whenever the covering transformation group is either residually finite or amenable. In the case when the covering transformation…
Varghese Mathai, Mel RothenbergJun 6, 1997
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