On certain principal directions in lightlike hypersurfaces of an indefinite Sasakian manifold

Abstract

In this paper, the geometry of some principal directions on a tangential lightlike hypersurface of an indefinite Sasakian manifold is investigated. In particular, we have proved, under some geometric conditions, that if the total space has constant holomorphic sectional curvature then such curvature is − 3. Moreover, it is shown that the underlying lightlike hypersurface is, locally, foliated by totally geodesic lightlike hypersurfaces.