On the structure vector field in lightlike hypersurfaces

We study lightlike hypersurfaces of an indefinite almost contact metric-manifold $\bar{M}$. We prove that there are only two types of such hypersurfaces, known as ascreen and inascreen, with respect to the position of the structure vector field of $\bar{M}$. We also show that the second class of hypersurfaces naturally admits an almost Hermitian structure.