The geometry of conformally Einstein metrics with degenerate Weyl tensor

Details The geometry of conformally Einstein metrics with degenerate Weyl tensor The geometry of conformally Einstein metrics with degenerate Weyl tensor

2006-08-24

arxiv.org/abs/math/0608598v1

Mathematics

Differential Geometry

24 pages, no figures

Scientific paper

The problem of characterizing conformally Einstein manifolds by tensorial conditions has been tackled recently in papers by M. Listing, and in work by A. R. Gover and P. Nurowski. Their results apply to metrics satisfying a "non-degeneracy" condition on the Weyl tensor \W. We investigate the geometry of the foliations arising on conformally Einstein spaces (with Riemannian signature) where this condition fails, which then allows us to characterize a general class of locally conformally Einstein Riemannian manifolds with degenerate Weyl tensor.

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