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Differential Geometry papers — page 4

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Integral Invariants of 3-Manifolds
This note describes an invariant of rational homology 3-spheres in terms of configuration space integrals which in some sense lies between the invariants of Axelrod and Singer and those of Kontsevich.
R. Bott, A. S. CattaneoOct 2, 1997
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PU(2) monopoles and relations between four-manifold invariants
Using quantum field-theoretic arguments, Witten has established a relation between the Donaldson and Seiberg-Witten invariants of smooth four-manifolds. In this survey article, we describe the…
Paul M. N. Feehan, Thomas G. LenessSep 30, 1997
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Corrigenda to: Introduction to Symplectic Topology
This contains a list of (mostly very minor) corrections to the book Introduction to Symplectic Topology, Clarendon Press, Oxford, (1995), together with rewritten versions of two lemmas and some…
Dusa McDuff, Dietmar SalamonSep 29, 1997
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Foliation by Constant Mean Curvature Spheres on Asymptotically Flat Manifolds
In this paper, the existence and uniqueness of foliations by constant mean curvature spheres on asymptotically flat manifolds of nonzero ADM mass in all dimensions were established. (A similar result…
Rugang YeSep 25, 1997
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Supplement on Curved flats in the space of point pairs and Isothermic surfaces: A Quaternionic Calculus
A quaternionic calculus for surface pairs in the conformal 4-sphere is elaborated. This calculus is then used to discuss the relation between curved flats in the symmetric space of point pairs and…
Udo Hertrich-JerominSep 24, 1997
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Investigation and application of the dressing action on surfaces of constant mean curvature
We investigate the dressing action on surfaces of constant mean curvature (CMC surfaces) in Euclidean space. In particluar, we show that for CMC surfaces with umbilics the isotropy group under…
Josef Dorfmeister, Guido HaakSep 22, 1997
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Linear transports along paths in vector bundles V. Properties of curvature and torsion
A geometric interpretation of curvature and torsion of linear transports along paths is presented. A number of (Bianchi type) identities satisfied by these quantities are derived. The obtained…
Bozhidar Z. IlievSep 20, 1997
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Transports along maps in fibre bundles
Generalized are the investigated in other works of the author transports along paths in fibre bundles to transports along arbitrary maps in them. Their structure and some properties are studied.…
Bozhidar Z. IlievSep 20, 1997
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Pseudo-Kaehler Quantization on Flag Manifolds
A unified approach to geometric, symbol and deformation quantizations on a generalized flag manifold endowed with an invariant pseudo-Kaehler structure is proposed. The Hilbert space of states is…
Alexander V. KarabegovSep 17, 1997
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Deformations of representations of fundamental groups of open Kaehler manifolds
Given a compact Kaehler manifold, we consider the complement U of a divisor with normal crossings. We study the variety of unitary representations of the fundamental group of U with certain…
Philip A. FothSep 10, 1997
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The First Eigenvalue of the Dirac Operator on Quaternionic Kaehler Manifolds
In a previous paper we proved a lower bound for the spectrum of the Dirac operator on quaternionic Kaehler manifolds. In the present article we show that the only manifolds in the limit case, i.e.…
W. Kramer, U. Semmelmann, G. WeingartSep 10, 1997
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From a Relativistic Phenomenology of Anyons to a Model of Unification of Forces via the Spencer Theory of Lie Structures
Starting from a relativistic phenomenology of anyons in crystals, we discuss the concept of relativistic interaction and the need to unify electromagnetism and gravitation within the Spencer…
Jacques L. RubinSep 8, 1997
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A Bernstein theorem for complete spacelike constant mean curvature hypersurfaces in Minkowski space
We obtain a gradient estimate for the Gauss maps from complete spacelike constant mean curvature hypersurfaces in Minkowski space into the hyperbolic space. As applications, we prove a Bernstein…
Huai-Dong Cao, Ying Shen, Shunhui ZhuSep 7, 1997
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continious cohomology of groups of volume-preserving and symplectic diffepmorphisms, measurable transfer and higher asymtotic cycles
I construct the real counterparts (which I call Borel-Bott classes) of the R/Z classes constructed in "Characteristic classes in symplectic topology", to appear, in the cohomology of…
Alexander ReznikovSep 6, 1997
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Euler class and free generation
the main theorem gives a sufficient condition for a n elements of SL(2,R) to generate a free group.The idea behind it is to use a nonorientable version of the Dehn-Wolpert-Goldman twist and to sew it…
Alexander ReznikovSep 6, 1997
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Irreducible constant mean curvature 1 surfaces in hyperbolic space with positive genus
In this work we give a method for constructing a one-parameter family of complete CMC-1 (i.e. constant mean curvature 1) surfaces in hyperbolic 3-space that correspond to a given complete minimal…
Wayne Rossman, Masaaki Umehara, Kotaro YamadaSep 2, 1997
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General existence of minimal surfaces of genus zero with catenoidal ends and prescribed flux
For each end of complete minimal surface in the Euclidean 3-space, the flux vector is defined. It is well-known that the sum of the flux vector over all ends are zero. Consider the following inverse…
Shin Kato, Masaaki Umehara, Kotaro YamadaSep 2, 1997
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An inverse problem of the flux for minimal surfaces
For a complete minimal surface in the Euclidean 3-space, the so-called flux vector corresponds to each end. The flux vectors are balanced, i.e., the sum of those over all ends are zero. Consider the…
Shin Kato, Masaaki Umehara, Kotaro YamadaSep 2, 1997
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Higher-Order Lagrangian Formalism on Grassmann Manifolds
The Lagrangian formalism on a arbitrary non-fibrating manifold is considered. The kinematical description of this generic situation is based on the concept of (higher-order) Grassmann manifolds which…
Dan Radu GrigoreSep 1, 1997
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Symplectic and contact Lie algebras with an application to Monge-Ampere equations
In this paper we consider symplectic and contact Lie algebras. We define contactization and symplectization procedures and describe its main properties. We also give classification of such algebras…
Boris KruglikovSep 1, 1997
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Kahler manifolds with large isometry group
We investigate compact Kahler manifolds, which are acted on by a semisimple compact Lie group G of isometries with one hypersurface orbit. In case of ordinary action and projectable complex…
F. Podesta', A. SpiroAug 31, 1997
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Ricci curvature, minimal surfaces and sphere theorems
Using an analogue of Myers' theorem for minimal surfaces and three dimensional topology, we prove the diameter sphere theorem for Ricci curvature in dimension three and a corresponding eigenvalue…
Ying Shen, Shunhui ZhuAug 30, 1997
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The structure of stable minimal hypersurfaces in Rn
We provide a new topological obstruction for complete stable minimal hypersurfaces in Rn. For n≥ 4, we prove that any complete orientable stable hypersurfaces in Rn has only one end. This…
Huai-Dong Cao, Ying Shen, Shunhui ZhuAug 30, 1997
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On the geometry and topology of manifolds of positive bi-Ricci curvature
We introduce some new curvature quantities such as conformal Ricci curvature and bi-Ricci curvature and extend the classical Myers theorem under these new curvature conditions. Moreover, we are able…
Ying Shen, Rugang YeAug 28, 1997
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Invariants of Velocities, and Higher Order Grassmann Bundles
An (r,n)-velocity is an r-jet with source at 0 ∈ n, and target in a manifold Y. An (r,n)-velocity is said to be regular, if it has a representative which is an immersion at $0 ∈…
Dan Radu Grigore, Demeter KrupkaAug 26, 1997
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