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.
Semisymmetric lightlike hypersurface, Ricci-semisymmetric lightlike hypersurface, pseudosymmetric lightlike hypersurface, pseudoparallel lightlike hypersurface
KAZAN, SEMA and ŞAHİN, BAYRAM
"Pseudosymmetric lightlike hypersurfaces,"
Turkish Journal of Mathematics: Vol. 38:
6, Article 9.
Available at: https://journals.tubitak.gov.tr/math/vol38/iss6/9