Symmetry properties of lightlike hypersurfaces in indefinite Sasakian manifolds

Abstract

. In this paper, we investigate symmetry properties of lightlike hypersurfaces in indefinite Sasakian manifolds, tangent to the structure vector field. Theorems on locally symmetric, semi-symmetric and Ricci semi-symmetric lightlike hypersurfaces are obtained. We show that, under some conditions, these hypersurfaces are totally geodesic. The non-existence conditions of specific lightlike hypersurfaces are given. We prove, under a certain condition, that in lightlike hypersurfaces of an indefinite Sasakian space form, tangent to the structure vector field, the local symmetry and semi-symmetry notions are equivalent. This equivalence is extended to the Ricci semi-symmetry notion when the lightlike hypersurfaces are considered to be η -totally umbilical.