de Sitter空间中具有常数量曲率的完备类空子流形

数学季刊 ›› 2009, Vol. 24 ›› Issue (3): 357-364.

de Sitter空间中具有常数量曲率的完备类空子流形

1. College of Mathematics and Information Science, Northwest Normal University2. Department of Mathematics, Hexi University

收稿日期:2007-02-01 出版日期:2009-09-30 发布日期:2023-06-27
作者简介: LIU Jian-cheng(1968- ), male, native of Zhenyuan, Gansu, a professor of Northwest Normal University, Ph.D., engages in differential geometry.
基金资助:
Supported by the NNSF of China(10871138)；

Complete Space-like Submanifolds with Constant Scalar Curvature in de Sitter Spaces

1. College of Mathematics and Information Science, Northwest Normal University2. Department of Mathematics, Hexi University

Received:2007-02-01 Online:2009-09-30 Published:2023-06-27
About author: LIU Jian-cheng(1968- ), male, native of Zhenyuan, Gansu, a professor of Northwest Normal University, Ph.D., engages in differential geometry.
Supported by:
Supported by the NNSF of China(10871138)；

摘要/Abstract

摘要： In this paper, we study the complete space-like submanifold Mⁿwith constant scalar curvature R≤c in the de Sitter space S_p^n+p(c) and obtain a pinching condition for Mn to be totally umbilical ones. The result generalizes that in [5,Main Theorem] to higher codimension and give a complement for n=2 there.

关键词: space-like submanifold, second fundamental form, scalar curvature

Abstract: In this paper, we study the complete space-like submanifold Mⁿwith constant scalar curvature R≤c in the de Sitter space S_p^n+p(c) and obtain a pinching condition for Mn to be totally umbilical ones. The result generalizes that in [5,Main Theorem] to higher codimension and give a complement for n=2 there.

Key words: space-like submanifold, second fundamental form, scalar curvature

中图分类号:

O186.12

刘建成, 张德燕. de Sitter空间中具有常数量曲率的完备类空子流形[J]. 数学季刊, 2009, 24(3): 357-364.

LIU Jian-cheng, ZHANG De-yan. Complete Space-like Submanifolds with Constant Scalar Curvature in de Sitter Spaces[J]. Chinese Quarterly Journal of Mathematics, 2009, 24(3): 357-364.

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