Spacelike submanifolds with parallel mean curvature vector in a de Sitter space \(S^{n+p}_{q}(c)\)

Journal of inequalities and applications

article

Junfeng Chen¹  Sanyang Liu¹  Shichang Shu² 

[1] School of Mathematics and Statistics, Xidian University;School of Mathematics and Information Science, Xianyang Normal University

关键词: De Sitter space;    Spacelike submanifold;    Totally umbilical;    Rigidity theorems;   

DOI  :  10.1186/s13660-020-02469-8

学科分类：电力

来源: SpringerOpen

【 摘 要 】

Spacelike submanifolds usually appear in the study of questions related to causality in general relativity. In this paper, we study an n-dimensional spacelike submanifold in $(n + p)$ -dimensional connected de Sitter space $S^{n+p}_{q}(c)$ of index q ( $1\leq q \leq p$ ) and of constant curvature c, and we obtain some integral inequalities of Simons type and rigidity theorems.

【 授权许可】

CC BY