Global properties of indefinite metrics with parallel Weyl tensor

Details Global properties of indefinite metrics with parallel Weyl tensor Global properties of indefinite metrics with parallel Weyl tensor

2007-08-30

arxiv.org/abs/0708.4211v1

in: Pure and Applied Differential Geometry - PADGE 2007, edited by F. Dillen and I. Van de Woestyne, Shaker Verlag, Aachen, 20

Mathematics

Differential Geometry

8 pages; page offset corrected

Scientific paper

This is an exposition of some recent results on ECS manifolds, by which we mean pseudo-Riemannian manifolds of dimensions greater than 3 that are neither conformally flat nor locally symmetric, and have parallel Weyl tensor. All ECS metrics are indefinite. We state two classification theorems, describing the local structure of ECS manifolds, and outline an argument showing that compact ECS manifolds exist in infinitely many dimensions greater than 4. We also discuss some properties of compact manifolds that admit ECS metrics, and provide a list of open questions about compact ECS manifolds.

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