Einstein-Weyl structures on lightike hypersurfaces

Cyriaque Atindogbe (1) , Lionel Bérard Bergery (1)

1 IECN - Institut Élie Cartan de Nancy

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.

Mots clés: Lightlike hypersurface; screen distribution; Einstein-Weyl structure

Domaines: Géométrie différentielle [math.DG]

Cyriaque Atindogbe, Lionel Bérard Bergery. Einstein-Weyl structures on lightike hypersurfaces. 2007. ⟨hal-00143466⟩