局部对称伪黎曼流形中的2-调和类空子流形

ON 2-HARMONIC SPACE-LIKE SUBMANIFOLDS IN A LOCALLY SYMMETRIC PSEUDO-RIEMANNIAN MANIFOLD

研究局部对称伪黎曼流形中的2-调和类空子流形,得到具有平行平均曲率向量子流形为极大的充分条件,紧致子流形的Simons型积分不等式,以及具有平行平均曲率向量的紧致子流形的全测性质。

This paper studies the 2-harmonic space-like submanifolds in a locally symmetric pseudo-Riemannian manifold,obtain the sufficient conditions of submanifolds with parallel mean curvature vector to be maximal submanifolds,the Simons' type integral inequality of compact submanifolds,and obtain that compact submanifolds with parallel mean curvature vector must be totally geodesic.-