Pseudo-umbilical time-like submanifolds in locally symmetric pseudo Riemann manifold

HuiRunBai

In this paper,  we  studied the pseudo-umbilical time-like SubmanifoldsMimmersed in a  locally symmetric pseudo Riemannian manifold.   when  is compact and with parallel mean  curvature vector,  the sufficient conditions for to be total geodesic are obtained by  using the Hopf  maximum principle.