Lightlike hypersurfaces of a semi-Riemannian manifold with a semi-symmetric metric connection

Abstract

In this study, we show that the connection induced on a lightlike hypersurface of a semi-Riemannian manifold with a semi-symmetric metric connection is semi-symmetric but not a metric connection and obtain the equations of Gauss and Codazzi. Then, we study conditions under which the Ricci tensor is symmetric and parallel.