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Differential Geometry papers — page 18

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On a class of Kähler manifolds whose geodesic flows are integrable
We study n-dimensional Kähler manifolds whose geodesic flows possess n first integrals in involution that are fibrewise hermitian forms and simultaneously normalizable. Under some mild…
Kazuyoshi KiyoharaSep 20, 1995
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Harmonic Maps with Prescribed Singularities on Unbounded Domains
The Einstein/Abelian-Yang-Mills Equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities 3Σk+1 into the…
Gilbert WeinsteinSep 19, 1995
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On the Geometry of Complex Grassmann Manifold, Its Noncompact Dual and Coherent States
Different topics on the differential geometry of the complex Grassmann manifold are surveyed in relation to the coherent states. A calculation of the tangent conjugate locus and conjugate locus in…
Stefan BerceanuSep 8, 1995
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Affine connections on involutive G-structures
This paper is a review of the twistor theory of irreducible G-structures and affine connections. Long ago, Berger presented a very restricted list of possible irreducibly acting holonomies of…
Sergey A. MerkulovSep 6, 1995
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On the Incompleteness of Berger's List of Holonomy Representations
In 1955, Berger Ber gave a list of irreducible reductive representations which can occur as the holonomy of a torsion-free affine connection. This list was stated to be complete up to possibly…
Quo-Shin Chi, Sergey A. Merkulov, Lorenz J. SchwachhöferAug 30, 1995
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Manin Triples for Lie Bialgebroids
In his study of Dirac structures, a notion which includes both Poisson structures and closed 2-forms, T. Courant introduced a bracket on the direct sum of vector fields and 1-forms. This bracket does…
Zhang-Ju Liu, Alan Weinstein, Ping XuAug 28, 1995
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Controlled Geometry via Smoothing
We prove that Riemannian metrics with a uniform weak norm can be smoothed to having arbitrarily high regularity. This generalizes all previous smoothing results. As a consequence we obtain a…
Peter Petersen, Guofang Wei, Rugang YeAug 23, 1995
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Uniton Bundles
We show that a twistor construction of Hitchin and Ward can be adapted to study unitons (harmonic spheres in a unitary group). Specifically, we show that unitons are equivalent to holomorphic bundles…
Christopher Kumar AnandAug 23, 1995
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Stiefel-Whitney Classes and the Conormal Cycle of a Singular Variety
A geometric construction of Sullivan's Stiefel-Whitney homology classes of a real analytic variety X is given by means of the conormal cycle of an embedding of X in a smooth variety. We prove…
Joseph H. G. Fu, Clint McCroryAug 21, 1995
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The Novikov-Bott inequalities
We generalize the Novikov inequalities for 1-forms in two different directions: first, we allow non-isolated critical points (assuming that they are non-degenerate in the sense of R.Bott), and,…
Maxim Braverman, Michael FarberAug 16, 1995
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Equivalence of Geometric and Combinatorial Dehn Functions
In this paper it is proved that if a finitely presented group acts properly discontinuously, cocompactly and by isometries on a simply connected Riemannian manifold, then the two Dehn functions, of…
Jose BurilloAug 15, 1995
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Rank one symmetric spaces and Rigidity
In this paper we show that if the limit set is not small ,marked length spectrum determines geometric structure of rank one locally symmetric manifolds.
Inkang KimAug 14, 1995
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Novikov type inequalities for differential forms with non-isolated zeros
We generalize the Novikov inequalities for 1-forms in two different directions: first, we allow non-isolated critical points (assuming that they are non-degenerate in the sense of R.Bott), and,…
Maxim Braverman, Michael FarberAug 14, 1995
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Introduction to Seiberg-Witten's Invariants, Part I: Theory of Spinors
In 1994, Witten has defined a monopole invariant and he has shown the equivalence of this invariant with Donaldson's polynomial using his result in \( \)-duality. This new invariant is very…
Jan Vacter YangAug 12, 1995
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On isometric and minimal isometric embeddings
In this paper we study critial isometric and minimal isometric embeddings of classes of Riemannian metrics which we call quasi-k-curved metrics. Quasi-k-curved metrics generalize the…
Thomas Ivey, J. M. LandsbergAug 9, 1995
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Quantization and Coherent States over Lagrangian Submanifolds
A membrane technique, in which the symplectic and Ricci forms are integrated over surfaces in a complexification of the phase space, as well a ``creation" connection with zero curvature over…
Mikhail V. KarasevAug 9, 1995
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Quantization of Kähler manifolds admitting H-projective mappings
We discuss the quantization of mechanical systems for which the Hamiltonian vector fields of observables form the deformation of n-dimensional oscilator algebra. Because of this fact these systems…
A. V. Aminova, D. A. KalininAug 4, 1995
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On the Ln 2-norm of Scalar Curvature
Comparisons on Ln 2-norms of scalar curvatures between Riemannian metrics and standard metrics are obtained. The metrics are restricted to conformal classes or under certain curvature…
Man Chun LeungAug 3, 1995
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On a Full Quantization of the Torus
I exhibit a prequantization of the torus which is actually a ``full'' quantization in the sense that a certain complete set of classical observables is irreducibly represented. Thus in this…
Mark J. GotayJul 31, 1995
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Localisation of the Donaldson's invariants along Seiberg-Witten classes
This article is a first step in establishing a link between the Donaldson polynomials and Seiberg-Witten invariants of a smooth 4-manifold.
Victor Pidstrigach, Andrei TyurinJul 24, 1995
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Cohomology of a Quaternionic Complex
We investigate the cohomology of a certain elliptic complex defined on a compact quaternionic-Kähler manifold with negative scalar curvature. We show that this particular complex is exact, with the…
Robin HoranJul 18, 1995
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Pin-structures on surfaces and quadratic forms
A correspondence between different Pin-type structures on a compact surface and quadratic (linear) forms on its homology is constructed. Addition of structures is defined and expressed in terms of…
A. Degtyarev, S. FinashinJul 10, 1995
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Curved flats in symmetric spaces
In this paper we study maps (curved flats) into symmetric spaces which are tangent at each point to a flat of the symmetric space. Important examples of such maps arise from isometric immersions of…
Dirk Ferus, Franz PeditJul 8, 1995
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Einstein Metrics on Complex Surfaces
We consider compact complex surfaces with Hermitian metrics which are Einstein but not Kaehler. It is shown that the manifold must be CP2 blown up at 1,2, or 3 points, and the isometry group of the…
Claude LeBrunJun 29, 1995
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Generalized Weierstrass formulae, soliton equations and Willmore surfaces. I. Tori of revolution and the mKdV equation
A new approach is proposed for study structure and properties of the total squared mean curvature W of surfaces in R3. It is based on the generalized Weierstrass formulae for inducing…
B. G. Konopelchenko, I. A. TaimanovJun 29, 1995
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