LIGHTLIKE HYPERSURFACES OF A LORENTZ MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

Abstract

Abstract. In this paper, we study lightlike hypersurfaces M of a Lorentzmanifold M with a semi-symmetric non-metric connection subject to theconditions; (1) the screen distribution S(TM) is totally geodesic in M,and (2) the second fundamental form B of M is parallel. 1. IntroductionThe notion of semi-symmetric non-metric connection on Riemannian man-ifolds was introduced by Ageshe and Chae. In [1], they studied some prop-erties of the curvature tensor of a Riemannian manifold endowed with a semi-symmetric non-metric connection. In [2], they gave basic properties of subman-ifolds of a Riemannian manifold endowed with a semi-symmetric non-metricconnection. Yasar, Coken and Yucesan [6] studied lightlike hypersurfaces ina semi-Riemannian manifold endowed with a semi-symmetric non-metric con-nection. They found the condition that the Ricci type tensor of a lightlikehypersurface of such a semi-Riemannian manifold be symmetric.In this paper, we study lightlike hypersurfaces Mof a Lorentz manifold Mendowed with a semi-symmetric non-metric connection subject to the condi-tions; (1) the screen distribution S(TM) is totally geodesic in M, and (2) thesecond fundamental form Bof Mis parallel. We prove the following result:Theorem 1.1. Let M be a lightlike hypersurface of a Lorentz manifold Madmitting a semi-symmetric non-metric connection. If the screen distributionS(TM) is totally geodesic in M and the second fundamental form Bof M isparallel, then Mis locally a product manifold L M