Pseudosymmetric lightlike hypersurfaces

Abstract

Abstract:We study lightlike hypersurfaces of a semi-Riemannian manifold satisfying pseudosymmetry conditions. We give sufficient conditions for a lightlike hypersurface to be pseudosymmetric and show that there is a close relationship of the pseudosymmetry condition of a lightlike hypersurface and its integrable screen distribution. We obtain that a pseudosymmetric lightlike hypersurface is a semisymmetric lightlike hypersurface or totally geodesic under certain conditions. Moreover, we give an example of pseudosymmetric lightlike hypersurfaces and investigate pseudoparallel lightlike hypersurfaces. Furthermore, we introduce Ricci-pseudosymmetric lightlike hypersurfaces, obtain characterizations, and give an example for such hypersurfaces.

Chaki type pseudo-symmetric lightlike hypersurfaces

“…Then one can see that if the conditions (19) and (20) are satisfied, then the condition (1) is also satisfied.…”

“…Many authors have studied such hypersurfaces in various semiRiemannian manifolds (see [23] and references therein). Recently, pseudo-symmetric lightlike hypersurfaces have been studied in the sense of Deszcz [19].…”