数学

局部对称伪黎曼流形中的极大类空子流形

  • 刘建成 ,
  • 王 凤
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  • 西北师范大学 数学与统计学院, 兰州  730070

收稿日期: 2015-12-22

  网络出版日期: 2017-01-13

基金资助

国家自然科学基金(11261051);
甘肃省高等学校基本科研业务费资助项目

Maximal space-like submanifolds in locally symmetric pseudo-Riemannian manifolds

  • LIU Jian-cheng ,
  • WANG Feng
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  • College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received date: 2015-12-22

  Online published: 2017-01-13

摘要

研究局部对称伪黎曼流形N^{n+p}_{p}中极大类空子流形 Mn. 当 Mn 紧致时, 得到了 Mn 是全测地子流形的一个充分条件. 当 Mn 完备非紧时, 给出了它的第二基本型模长平方的一个拼挤定理.

本文引用格式

刘建成 , 王 凤 . 局部对称伪黎曼流形中的极大类空子流形[J]. 华东师范大学学报(自然科学版), 2016 , 2016(6) : 119 -126 . DOI: 10.3969/j.issn.1000-5641.2016.06.013

Abstract

In this article we study the maximal space-like submanifold Mn which is isometrically immersed into locally symmetric pseudo-Riemannian manifold Nn+p
p . One main theroem is a sufficient condition for compact Mn to be totally geodesic ones. We also prove a pinching theorem for the square length of the second fundamental form when Mn is complete.

参考文献

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