Null hypersurface normalized by the structure vector field in a para-Sasakian manifold

Abstract

 We examine the geometry of a null hypersurface $M$ of a para-Sasakian manifold $(\overline{M},\overline{\phi}, K, \overline{\eta},\overline{g})$ transversal to the structure vector field $K$. The {later} is then a rigging $\zeta$ for $M$, and $M$ is called $K$-normalized null hypersurface. We characterize the geometry of such a null hypersurface and prove under some conditions that there exist leaves of an integrable distribution of the screen distribution admitting an almost para complex structure. Also, we derive certain non-existence results and discuss some properties of semi-symmetric(resp. locally symmetric) $K$-normalized null hypersurfaces of para-Sasakian manifolds, for instance, we demonstrate that any para-Sasakian manifold admitting a semi-symmetric totally geodesic $K$-normalized null hypersurface is of constant negative curvature along the null hypersurface.