华东师范大学学报（自然科学版） >

2016 , Vol. 2016 >Issue 6: 119 - 126

DOI: https://doi.org/10.3969/j.issn.1000-5641.2016.06.013

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

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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

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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.

关键词： 局部对称; 极大; 类空; 全测地

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.

Key words： locally symmetric; maximal; space-like; totally geodesic

参考文献

[ 1 ] CALABI E. Examples of Bernstein problems for some nonlinear equations[J]. Proc Symp Pure Appl Math, 1970,15: 223-230.
[ 2 ] CHENG S Y, YAU S T. Maximal space-like hypersurfaces in the Lorentz Minkowski spaces[J]. Ann of Math,1976, 104: 407-419.
[ 3 ] ISHIHARA T. Maximal spacelike submanifolds of a pseudo-Riemannian space of constant curvature[J]. Michigan Math J, 1988, 35: 345-352.
[ 4 ] SUN H F. On maximal spacelike submanifolds[J]. J of Geom, 1999, 65: 193-199.
[ 5 ] CHENG Q M, ISHIKAWA S. Complete maximal spacelike submanifolds[J]. Kodai Math J, 1997, 20: 208-217.
[ 6 ] NISHIKAWA S. On maximal spacelike hypersurfaces in a Lorentzian manifold[J]. Nagoya Math J, 1984, 95: 117-124.
[ 7 ] 张志兵, 陈抚良. 局部对称黎曼流形中的极小子流形[J].纯粹数学与应用数学, 2013, 29: 373-381.
[ 8 ] WALI A N, AKANGA J R. Some results on totally real maximal spacelike submanifolds of an indefinite complex space form[J]. Int J Math Anal, 2011, 5: 207-213.
[ 9 ] 吕艳, 廖蔡生. 局部对称空间中极小子流形的一点补充[J].华东师范大学学报(自然科学版), 2003(4): 5-11.
[10] LIU J C, SUN Z Y. On spacelike hypersurfaces with constant scalar curvature in locally symmetric Lorentz spaces[J]. J Math Anal Appl, 2010, 364: 195-203.
[11] GOLDBERG S I. Curvature and Homology[M]. London: Academic Press, 1962: 92-94.
[12] OMORI H. Isometric immersions of Riemannian manifolds[J]. J Math Soc Japan, 1967, 19: 205-214.
[13] AIYAMA R. The generalized Gauss map of a space-like submanifold with parallel mean curvature vector in a pseudo-Euclidean space[J]. Japan J Math, 1994, 20: 93-114.
[14] AIYAMA R. Compact space-like m-submanifolds in a pseudo-Riemannian sphere Sm+p p (c)[J]. Tokyo J Math, 1995, 18: 81-90.
[15] XU S L, HU Z S. Compact maximal space-like submanifolds in a pseudo-Riemannian spacetime Sm+p p [J]. Northeast Math J, 2006, 22: 253-259.

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