  In this study, we obtain a spinorial Gauss formula for a lightlike
hypersurface in Lorentzian manifold with 4-dimension. Then, we take into
account the changes caused by degenerate metric on hypersurface and investigate
Dirac operator for lightlike hypersurface. Later, we establish the relation
between Dirac operators and Riemannian curvatures of manifold and hypersurface.
