局部对称伪黎曼流形中常数量曲率的完备类空子流形  

Complete Space-like Submanifolds with Constant Scalar Curvature in a Locally Symmetric Pesudo-Riemannian Manifold

作　　者：张佳佳[1] 

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241000

出　　处：《安庆师范学院学报（自然科学版）》2011年第4期21-25,共5页Journal of Anqing Teachers College(Natural Science Edition)

摘　　要：本文研究了局部对称伪黎曼流形Npn+p中常数量曲率的完备类空子流形Mn,主要利用丘成桐的广义极大值原理和自伴算子讨论了关于第二基本形式模长平方S的pinching问题,得到Mn成为全测地的刚性定理。In this paper,we study the complete space-like submanifolds Mn with constant scalar curvature in a locally symmetric pesudo-Riemannian manifold Nn＋pp.We discuss the pinching problem on the square of the length of the second fundamental form S mainly by making use of the generalized maximal principle of Yau and self-adjoint operator,and obtain a rigidity theorem for Mn being totally geodesic.

关 键 词：局部对称 伪黎曼流形 常数量曲率 全测地 

分 类 号：O186.14[理学—数学]