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Impossible Einstein-Weyl geometries

Eastwood, Michael (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

In the joint paper of the author with K. P. Tod [J. Reine Angew. Math. 491, 183-198 (1997; Zbl 0876.53029)] they showed all local solutions of the Einstein-Weyl equations in three dimensions, where the background metric is homogeneous with unimodular isometry group. In particular, they proved that there are no solutions with Nil or Sol as background metric. In this note, these two special cases are presented.

Integrability of the Poisson algebra on a locally conformal symplectic manifold

Haller, Stefan, Rybicki, Tomasz (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

Summary: It is proven that the Poisson algebra of a locally conformal symplectic manifold is integrable by making use of a convenient setting in global analysis. It is also observed that, contrary to the symplectic case, a unified approach to the compact and non-compact case is possible.

Introduction

J. C. Saut, R. Temam (1989)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Introduction

John Oprea, Aleksy Tralle (1998)

Banach Center Publications

Invariance properties of the Laplace operator

Eichhorn, Jürgen (1990)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] The paper deals with a special problem of gauge theory. In his previous paper [The invariance of Sobolev spaces over noncompact manifolds, Partial differential equations, Proc. Symp., Holzhaus/GDR 1988, Teubner- Texte Math. 112, 73-107 (1989; Zbl 0681.58011)], the author introduced the Sobolev completions 𝒞 ¯ P k of the space 𝒞 P of all G-connections on a G-principal fibre bundle P. In the present paper, under the assumption of bounded curvatures and their...

Invariant orders in Lie groups

Neeb, Karl-Hermann (1991)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0742.00067.]The author formulates several theorems about invariant orders in Lie groups (without proofs). The main theorem: a simply connected Lie group G admits a continuous invariant order if and only if its Lie algebra L ( G ) contains a pointed invariant cone. V. M. Gichev has proved this theorem for solvable simply connected Lie groups (1989). If G is solvable and simply connected then all pointed invariant cones W in L ( G ) are global in G (a Lie wedge W ⊂ L ( G ) is said to...

Isometric immersions and induced geometric structures

D‘Ambra, G. (1999)

Proceedings of the 18th Winter School "Geometry and Physics"

In the paper under review, the author presents some results on the basis of the Nash-Gromov theory of isometric immersions and illustrates how the same results and ideas can be extended to other structures.

Isotropy representation of flag manifolds

Alekseevsky, D. V. (1998)

Proceedings of the 17th Winter School "Geometry and Physics"

A flag manifold of a compact semisimple Lie group G is defined as a quotient M = G / K where K is the centralizer of a one-parameter subgroup exp ( t x ) of G . Then M can be identified with the adjoint orbit of x in the Lie algebra 𝒢 of G . Two flag manifolds M = G / K and M ' = G / K ' are equivalent if there exists an automorphism φ : G → G such that φ ( K ) = K ' (equivalent manifolds need not be G -diffeomorphic since φ is not assumed to be inner). In this article, explicit formulas for decompositions of the isotropy representation for all flag manifolds...

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