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In this paper, we study the geometry of lightlike hypersurfaces of an indefinite Sasakian manifold. The main result is to prove three characterization theorems for such a lightlike hypersurface. In addition to these main theorems, we study the geometry of totally geodesic lightlike hypersurfaces of an indefinite Sasakian manifold.

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Abstract. In this paper, we study lightlike hypersurfaces of an indefinite Sasakian manifoldM . First, we construct a type of lightlike hypersurface according to the form of the structure vector field ofM , named by ascreen lightlike hypersurface. Next, we characterize the geometry of such ascreen lightlike hypersurfaces.