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Differential Geometry papers

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Classification of stationary compact homogeneous special pseudo Kähler manifolds of semisimple groups
The variation of Hodge structure of a Calabi-Yau 3-fold induces a canonical Kähler metric on its Kuranishi moduli space, known as the Weil-Petersson metric. Similarly, special pseudo Kähler manifolds…
D. V. Alekseevsky, V. CortesMay 26, 1999
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Equivariant K-Theory of Simply Connected Lie Groups
We compute the equivariant K-theory KG*(G) for a simply connected Lie group G (acting on itself by conjugation). We prove that KG*(G) is isomorphic to the algebra of Grothendieck…
Jean-Luc Brylinski, Bin ZhangMar 3, 1999
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Continuous families of isospectral metrics on simply connected manifolds
We construct continuous families of Riemannian metrics on certain simply connected manifolds with the property that the resulting Riemannian manifolds are pairwise isospectral for the Laplace…
Dorothee SchuethJan 1, 1999
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The beta function of a knot
We introduce the beta function of a knot in euclidean three-space. This is a meromorphic function of a complex variable which we prove admits a Bernstein type functional equation. We determine the…
Jean-Luc BrylinskiFeb 3, 1998
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Prescribing Mean Curvature: Existence and Uniqueness Problems
This paper presents results on the extent to which mean curvature data can be used to determine a surface in space or its shape. The emphasis is on Bonnet's problem: classify and study the…
George I. KamberovFeb 1, 1998
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On the Spinor Representation of Surfaces in Euclidean 3-Space
The aim of the present paper is to clarify the relationship between immersions of surfaces and solutions of the inhomogeneous Dirac equation. The main idea leading to the description of a surface M2…
Thomas FriedrichDec 30, 1997
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Weinstein Conjecture and GW Invariants
In this paper, we establish a general relationship between the nonvanishing of GW invariants with the existence of the closed orbits of a Hamiltonian system. As an application, we completely solved…
Gang Liu, Gang TianDec 30, 1997
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Quadratic Differentials, Quaternionic Forms, and Surfaces
Global isothermic immersions are defined and studied with the aid of a connection between quadratic differentials and immersions. The applications are two problems stemming from the fundamental…
George I. KamberovDec 30, 1997
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The minimum principle from a Hamiltonian point of view
Let G be a complex Lie group, GR a real form of G and X a GR-stable domain of holomorphy in a complex G-manifold. If there is a GR-invariant strictly plurisubharmonic function on X which has…
Peter HeinznerDec 28, 1997
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New families of conservative systems on S2 possessing an integral of fourth degree in momenta
There is a well-known example of integrable conservative system on S2, the case of Kovalevskaya in the dynamics of a rigid body, possessing an integral of fourth degree in momenta. Goryachev…
Elena N. SelivanovaDec 27, 1997
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Jacobi vector fields of integrable geodesic flows
We show that an invariant surface allows to construct the Jacobi vector field along a geodesic and construct the formula for the normal component of the Jacobi field. If a geodesic is the transversal…
V. S. Matveev, P. J. TopalovDec 23, 1997
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Simple Type and the Boundary of Moduli Space
We measure, in two distinct ways, the extent to which the boundary region of moduli space contributes to the ``simple type'' condition of Donaldson theory. Using a geometric representative of…
David Groisser, Lorenzo SadunDec 22, 1997
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Simple Type is Not a Boundary Phenomenon
This is an expository article, explaining recent work by D. Groisser and myself [GS] on the extent to which the boundary region of moduli space contributes to the ``simple type'' condition of…
Lorenzo SadunDec 22, 1997
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Parallel Connections Over Symmetric Spaces
Let M be a simply connected Riemannian symmetric space, with at most one flat direction. We show that every Riemannian (or unitary) vector bundle with parallel curvature over M is an associated…
Luis Guijarro, Lorenzo Sadun, Gerard WalschapDec 22, 1997
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Double Lie algebroids and second-order geometry, II
We complete the construction of the double Lie algebroid of a double Lie groupoid begun in the first paper of this title. We show that the Lie algebroid structure of an LA--groupoid may be prolonged…
Kirill C. H. MackenzieDec 22, 1997
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Integration of Lie bialgebroids
We prove that under certain mild assumptions a Lie bialgebroid integrates to a Poisson groupoid. This includes, in particular, a new proof of the existence of local symplectic groupoids for any…
Kirill C. H. Mackenzie, Ping XuDec 22, 1997
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Weyl groups of Hamiltonian manifolds, I
We consider a connected compact Lie group K acting on a symplectic manifold M such that a moment map m exists. A pull-back function via m Poisson commutes with all K-invariants. Guillemin-Sternberg…
Friedrich KnopDec 20, 1997
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Notes on affine isometric actions of discrete groups
Consider a lattice Γ in a group G = SL2(), SO(1,n), SU(1,n), SL2(p). We discuss actions of Γ by affine isometric transformations of Hilbert spaces. We show that for irreducible affine…
Yurii A. NeretinDec 20, 1997
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The decomposition and classification of radiant affine 3-manifolds
An affine manifold is a manifold with torsion-free flat affine connection. A geometric topologist's definition of an affine manifold is a manifold with an atlas of charts to the affine space with…
Suhyoung ChoiDec 19, 1997
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Projectivity of moment map quotients
Let G be a complex reductive group and K a maximal compact subgroup. If X is a smooth projective G-variety, with a fixed (not necessarily integral) K-invariant Kaehler form, then the K-action is…
Peter Heinzner, Luca MiglioriniDec 19, 1997
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The functional definition of geodesics
In this paper a functional definition of geodesics is introduced which allows to generalize the notion of a geodesic from smooth to topological manifolds. It is shown that in the smooth case the new…
L. KlapkaDec 19, 1997
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PU(2) monopoles. II: Top-level Seiberg-Witten moduli spaces and Witten's conjecture in low degrees
In this article we complete the proof---for a broad class of four-manifolds---of Witten's conjecture that the Donaldson and Seiberg-Witten series coincide, at least through terms of degree less…
Paul M. N. Feehan, Thomas G. LenessDec 8, 1997
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The Weierstrass representation of closed surfaces in R3
In the present paper which a sequel to dg-ga/9511005 and dg-ga//9610013 a global Weierstrass representation of an arbitrary closed oriented surface of genus ≥ 1 in the the three-space is…
Iskander A. TaimanovDec 6, 1997
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Generalized Symmetries of Partial Differential Equations and Quasiexact Solvability
Using the adjoint action of the infinitesimal translations (with respect to some (in)dependant variables) on specific finite-dimensional subspaces of the space of generalized symmetries of some…
Arthur G. SergheyevDec 4, 1997
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Positively curved 7-dimensional manifolds
We deal with seven dimensional compact Riemannian manifolds of positive curvature which admit a cohomogeneity one action by a compact Lie group G. We prove that the manifold is diffeomorphic to a…
Fabio Podesta, Luigi VerdianiDec 4, 1997
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