Normalized Null hypersurfaces of Indefinite Kähler Manifolds

We study null hypersurfaces of indefinite Kähler manifolds and by taking the advantages almost complex structure $J$, we select a suitable rigging $\zeta$, which call $J-$rigging, on hypersurface. This enables us to build an associated Hermitian metric $\breve{g}$ ambient space is restricted into non-degenerated $\widetilde{g}$ normalized derive Gauss-Weingarten type formulae for hypersurface $M$ manifold $\overline{M}$ with fixed closed Killing $J-$rigging $M$. Later, establish some relations linking curvatures, sectional Ricci scalar curvatures etc.