局部对称黎曼流形中某类超曲面的刚性定理

J4 ›› 2009, Vol. 47 ›› Issue (6): 1125-1129.

局部对称黎曼流形中某类超曲面的刚性定理

华义平, 宋卫东

安徽师范大学数学计算机科学学院, 安徽芜湖 241000

收稿日期:2009-01-07 出版日期:2009-11-26 发布日期:2010-01-07
通讯作者: 宋卫东 E-mail:swd56@sina.com.

Rigidity Theorems for Some Hypersurfaces ina Locally Symmetric Manifold

HUA Yiping, SONG Weidong

College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, Anhui Province, China

Received:2009-01-07 Online:2009-11-26 Published:2010-01-07
Contact: SONG Weidong E-mail:swd56@sina.com.

摘要/Abstract

摘要：

讨论局部对称黎曼流形中Cheng-Yau算子□的自伴性, 并应用该算子研究局部对称空间中的紧致超曲面, 获得了一个积分不等式及一些刚性定理.

关键词: 局部对称；超曲面；自伴算子；数量曲率；全脐

Abstract:

The authors discussed the ChengYau’s selfadjoint operator □ in a locally symmetric Riemannian manifold, and applied this operator to investigating some compact hypersurfaces, obtaining a integral inequality and some rigidity theorems.

Key words: locally symmetric, hypersurfaces, selfadjoint operator, scalar curvature, totally umbilical

中图分类号:

O186.12

华义平, 宋卫东. 局部对称黎曼流形中某类超曲面的刚性定理[J]. J4, 2009, 47(6): 1125-1129.

HUA Yiping, SONG Weidong. Rigidity Theorems for Some Hypersurfaces ina Locally Symmetric Manifold[J]. J4, 2009, 47(6): 1125-1129.