Einstein-Weyl structures on lightike hypersurfaces

Details Einstein-Weyl structures on lightike hypersurfaces Einstein-Weyl structures on lightike hypersurfaces

2007-04-25

arxiv.org/abs/0704.3383v1

Mathematics

Differential Geometry

soumis

Scientific paper

We study Weyl structures on lightlikes hypersurfaces endowed with a conformal structure of certain type and specific screen distribution: the Weyl screen structures. We investigate various differential geometric properties of Einstein-Weyl screen structures on lightlike hypersurfaces and show that, for ambiant Lorentzian space $\mathbb{R}^{n+2}_{1}$ and a totally umbilical screen foliation, there is a strong interplay with the induced (Riemannian) Weyl-structure on the leaves. Finally, we establish necessary and sufficient conditions for a Weyl structure defined by the $1-$form of an almost contact structure given by an additional complex structure in case of an ambiant Kaehler manifold to be closed.

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