Abstract: We first establish a integral inequality for compact maximal space-like subman ifolds in pseudo-Riemannian manifolds N_p^n+p. Then, we investigate compact space-like sub manifolds and hupersurfaces with parallel second fundamental form in N_p^n+p and some other ambient spaces. We obtain some distribution theorems for the square norm of the second fundamental form.

Key words: pseudo-Riemannian , manifold;submanifold;hypersurface;parallel , second , fun- damental form;space-like