PSEUDO-SPHERICAL SUBMANIFOLDS OF PSEUDO-EUCLIDEAN SPACE

Decomposing the position vectors of a submanifold into the tangential and normal components,the present paper studies the conditions under which a compact space-like submanifold of pseudo-Euclidean space is pseudo-spherical submanifold.It is observed that the tangential components of the position vectors being harmonic and the support function of the submanifold being contant provides two necessary and sufficient conditions.At the same time,we obtain another necessary and sufficient condition for the submanifold with parallel mean curvature vector.Specially,we also study Chen submanifold and obtain that if its mean curvature vector is parallel and not isotropic and the support function doesn't chang its sign,it is pseudo-spherical submanifold.