Pseudo-parallel space-like submanifolds of pseudo-Riemannian space forms

The main purpose of this paper is to study space-like submanifolds of pseudo-Riemannian space forms.A necessary and sufficient condition for space-like hypersurfaces to be pseudo-parallel ones is obtained.Using Jordan triple system,a sufficient condition for pseudo-parallel space-like submanifolds to be totally geodesic ones is also given.