伪黎曼流形中具有平行平均曲率向量的伪脐子流形  

Pseudo-Umbilical Submanifolds with Parallel Mean Curvature Vector in Pseudo-Riemannian Manifold

作　　者：戴慧[1] 

机构地区：[1]安徽师范大学数学与计算机科学学院,安徽芜湖241000

出　　处：《安徽师范大学学报（自然科学版）》2008年第1期20-24,共5页Journal of Anhui Normal University(Natural Science)

基　　金：安徽省教育厅自然科学研究重点项目(2004kj166zd)

摘　　要：研究了伪黎曼流形中具有平行平均曲率向量的伪脐子流形,Npn+p为n+p维完备连通伪黎曼流形,它的截面曲率KN满足a≤KN≤b,Mn为Npn+p中紧致的具有平行平均曲率向量的伪脐子流形.通过利用Green散度定理,得到了一个J.Simons型积分不等式,推广了已有结果.In this paper, the pseudo-umbilical submanifolds with parallel mean curvature vector in pseudo-Riemannian manifold is discussed. Let Nn^n＋p be an n ＋ p-dimensional, complete and connected pseudo- Riemannian manifold, whose sectional curvature KN satisfies a ≤ KN≤ b. Let M^n be a compact pseudo- umbilical submanifolds with parallel mean curvature vector in Np^n＋p. By applying Green divergence theorem, an integral inequality of Simons＇ type is obtained.

关 键 词：伪黎曼流形 伪脐子流形 平行平均曲率向量 

分 类 号：O186[理学—数学]