On $\zeta$-Normalized Null Hypersurfaces of Indefinite Sasakian Manifolds

We examine null hypersurfaces that are normalized by the structure vector field $\zeta$ (briefly, $\zeta$-normalized null hypersurfaces) in almost contact metric manifolds. We characterize the geometry of such null hypersurfaces, and an example is provided. We show that leaves of an integrable screen distribution within these hypersurfaces admit an almost contact metric structure $(\psi,h,\nu,U,)$. In cases where the ambient space is an indefinite Sasakian, we show that it is not always possible to choose a structure vector field with specific geometric properties, along with prescribed geometric properties for the null hypersurface. The necessary and sufficient condition for normality of $(\psi,h,\nu,U,)$-structure is established. Integrability conditions for the distributions on a $\zeta$-normalized null hypersurface of an indefinite Sasakian manifolds are investigated.