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Turkish Journal of Mathematics

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.

DOI

10.3906/mat-1311-19

Keywords

Semisymmetric lightlike hypersurface, Ricci-semisymmetric lightlike hypersurface, pseudosymmetric lightlike hypersurface, pseudoparallel lightlike hypersurface

First Page

1050

Last Page

1070

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