伪黎曼空间型中具有常数量曲率的类空子流形

doi:10.6040/j.issn.1671-9352.0.2017.021

山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (10): 89-96.doi: 10.6040/j.issn.1671-9352.0.2017.021

伪黎曼空间型中具有常数量曲率的类空子流形

文海燕,刘建成

西北师范大学数学与统计学院, 甘肃兰州 730070

收稿日期:2017-01-23 出版日期:2017-10-20 发布日期:2017-10-12
作者简介:文海燕(1992— ), 女, 硕士研究生, 研究方向为微分几何. E-mail:wenhy1992@foxmail.com
基金资助:
国家自然科学基金资助项目(11261051)

Space-like submanifolds with constant scalar curvature in the pseudo-Riemannian space forms

WEN Hai-yan, LIU Jian-cheng

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China

Received:2017-01-23 Online:2017-10-20 Published:2017-10-12

摘要/Abstract

摘要： 设M ⁿ是伪黎曼空间型N ^n+p_q(c)(1≤q≤p)中具有常数量曲率R的n维完备类空子流形。假定M ⁿ在N ^n+p_q(c)中的第二基本形式是局部类时的情况下, 应用Simons型不等式以及Cheng-Yau引进的二阶微分算子, 得到了M ⁿ的一个刚性结果。

关键词: 伪黎曼空间型, 类空子流形, 第二基本形式, 常数量曲率

Abstract: Let M ⁿ be a space-like submanifold immersed in a pseudo-Riemannian space form N ^n+p_q(c) with constant scalar curvature. Assume the second fundamental form of M ⁿ in N ^n+p_q(c) is locally time-like, by applying Simons inequality and Cheng-Yau modified operator, a rigidity theorem of M ⁿ is obtained.

Key words: pseudo-Riemannian space form, space-like submanifold, constant scalar curvature, the second fundamental form

中图分类号:

O186.12

文海燕,刘建成. 伪黎曼空间型中具有常数量曲率的类空子流形[J]. 山东大学学报（理学版）, 2017, 52(10): 89-96.

WEN Hai-yan, LIU Jian-cheng. Space-like submanifolds with constant scalar curvature in the pseudo-Riemannian space forms[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 89-96.

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伪黎曼空间型中具有常数量曲率的类空子流形

Space-like submanifolds with constant scalar curvature in the pseudo-Riemannian space forms

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