局部对称伪黎曼流形中的极大类空子流形

Maximal space-like submanifolds in locally symmetric pseudo-Riemannian manifolds

研究局部对称伪黎曼流形N_p^(n+p)中极大类空子流形M^n.当M^n紧致时,得到了M^n是全测地子流形的一个充分条件.当M^n完备非紧时,给出了它的第二基本型模长平方的一个拼挤定理.

In this article we study the maximal space-like submanifold M^n which is isometrically immersed into locally symmetric pseudo-Riemannian manifold Np^n＋p. One main theroem is a sufficient condition for compact Ms to be totally geodesic ones. We also prove a pinching theorem for the square length of the second fundamental form when M^n is complete.