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Differential Geometry papers — page 12

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Coordinates on Schubert cells, Kostant's harmonic forms, and the Bruhat-Poisson structure on G/B
We relate Kostant's theorem on the cohomology of a flag manifold G/B with the geometry of the Bruhat-Poisson structure. We express Kostant's harmonic forms in terms of the moment maps (for…
Jiang-Hua LuOct 18, 1996
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Transverse measures, the modular class, and a cohomology pairing for Lie algebroids
We show that every Lie algebroid A over a manifold P has a natural representation on the line bundle QA = topA top T*P. The line bundle QA may be viewed as the…
Sam Evens, Jiang-Hua Lu, Alan WeinsteinOct 16, 1996
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De Rham theorem for extended L2-cohomology
We prove an analogue of the de Rham theorem for the extended L2-cohomology introduced by M. Farber. This is done by establishing that the de Rham complex over a compact closed manifold with…
Mikhail ShubinOct 11, 1996
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Bonnet pairs and isothermic surfaces
In this note we classify all Bonnet pairs on a simply connected domain. Our main intent was to apply what we call a quaternionic function theory to a concrete problem in differential geometry. The…
George Kamberov, Franz Pedit, Ulrich PinkallOct 9, 1996
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The Spinor Representation of Surfaces in Space
The spinor representation is developed for conformal immersions of Riemann surfaces into space. We adapt the approach of Dennis Sullivan, which treats a spin structure on a Riemann surface M as a…
Rob Kusner, Nick SchmittOct 8, 1996
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Moduli Spaces of Embedded Constant Mean Curvature Surfaces with Few Ends and Special Symmetry
We give necessary conditions on complete embedded surfaces with three or four ends subject to reflection symmetries. The respective submoduli spaces are two-dimensional varieties in the moduli…
K. Brauckmann, R. KusnerOct 8, 1996
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Groups quasi-isometric to symmetric spaces
We determine the structure of finitely generated groups which are quasi-isometric to symmetric spaces of noncompact type, allowing Euclidean de Rham factors If X is a symmetric space of noncompact…
Bruce Kleiner, Bernhard LeebOct 6, 1996
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Determinant lines, von Neumann algebras and L2 torsion
In this paper, we suggest a construction of determinant lines of finitely generated Hilbertian modules over finite von Neumann algebras. Nonzero elements of the determinant lines can be viewed as…
A. Carey, M. Farber, V. MathaiOct 3, 1996
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Abelian Chern-Simons theory
We give a construction of the abelian Chern-Simons gauge theory from the point of view of a 2+1 dimensional topological quantum field theory. The definition of the quantum theory relies on geometric…
Mihaela ManoliuOct 1, 1996
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Quantization of symplectic tori in a real polarization
We apply the geometric quantization method with real polarizations to the quantization of a symplectic torus. By quantizing with half-densities we canonically associate to the symplectic torus a…
Mihaela ManoliuSep 30, 1996
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The spectrum of Kleinian manifolds
A Kleinian manifold Y is a quotient of a rank-one symmetric space of non-compact type by a convex-cocompact discrete group of isometries. We describe the spectral decomposition of the space of square…
U. Bunke, M. OlbrichSep 30, 1996
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On a theorem by do Carmo and Dajczer
We give a new proof of a theorem by M.P. do Carmo and M. Dajczer on helicoidal surfaces of constant mean curvature.
Guido HaakSep 25, 1996
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On index formulas for manifolds with metric horns
In this paper we discuss the index problem for geometric differential operators (Spin-Dirac operator, Gauß-Bonnet operator, Signature operator) on manifolds with metric horns. On singular manifolds…
Matthias Lesch, Norbert PeyerimhoffSep 24, 1996
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Deforming a map into a harmonic map
Using a flow first introduced by J.P. Anderson, we obtain some existence theorems for harmonic maps from a noncompact complete Riemannian manifold into a complete Riemannian manifold. In particular,…
Deane YangSep 21, 1996
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Great sphere foliations and manifolds with curvature bounded above
The survey is devoted to Toponogov's conjecture, that if a complete simply connected Riemannian manifold with sectional curvature 4 and injectivity radius π/2 has extremal…
Vladimir Y. Rovenskii, Victor A. ToponogovSep 20, 1996
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On constant mean curvature surfaces with periodic metric
We investigate CMC-surfaces with periodic metric in a dressing orbit of the cylinder. It is shown, that such surfaces are always of finite type. Using the periodicity conditions for the extended…
Josef Dorfmeister, Guido HaakSep 20, 1996
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Stiefel-Whitney Currents
A canonically defined mod 2 linear dependency current is associated to each collection of m sections of a real rank n vector bundle. This current is supported on the linear dependency set of the…
Reese Harvey, John ZweckSep 17, 1996
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Approximating L2 invariants of amenable covering spaces: A combinatorial approach
In this paper, we prove that the L2 Betti numbers of an amenable covering space can be approximated by the average Betti numbers of a regular exhaustion, proving a conjecture that we made in an…
Jozef Dodziuk, Varghese MathaiSep 16, 1996
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Spinors, Nonlinear Connections, and Nearly Autoparallel Maps of Generalized Finsler Spaces
We review the geometric setting of the field theory with locally anisotropic interactions. The concept of locally anisotropic space is introduced as a general one for various type of extensions of…
Sergiu I. VacaruSep 16, 1996
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Approximating L2 invariants of amenable covering spaces: A heat kernel approach
In this paper, we prove that the L2 Betti numbers of an amenable covering space can be approximated by the average Betti numbers of a regular exhaustion, under some hypotheses. We also prove that…
Jozef Dodziuk, Varghese MathaiSep 6, 1996
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On the eta-invariant of certain nonlocal boundary value problems
Motivated by the work of Vishik on the analytic torsion we introduce a new class of generalized Atiyah-Patodi-Singer boundary value problems. We are able to derive a full heat expansion for this…
Jochen Brüning, Matthias LeschSep 4, 1996
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Kaehler structures on Kc/(P,P)
Let K be a compact semi-simple Lie group. We classify K-invariant Kaehler structures on the space Kc/(P,P), where Kc is the complexification of K, P is a parabolic subgroup of Kc, and (P,P) the…
Meng-Kiat ChuahAug 28, 1996
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Stability of symmetric tops via one variable calculus
We study the stability of symmetric trajectories of a particle on the Lie group SO(3) whose motion is governed by an SO(3)× SO(2) invariant metric and an SO(2)× SO(2) invariant…
Eugene LermanAug 28, 1996
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A universal lower bound for the first eigenvalue of the Dirac operator on quaternionic Kaehler manifolds
A universal lower bound for the first positive eigenvalue of the Dirac operator on a compact quaternionic Kaehler manifold M of positive scalar curvature is calculated. It is shown that it is equal…
Wolfram KramerAug 28, 1996
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Discriminants of convex curves are homeomorphic
For a given real generic curve : S1 RPn let D denote the ruled hypersurface in RPn consisting of all osculating subspaces to of codimension 2. A curve $:…
B. ShapiroAug 26, 1996
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