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

[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.

[学科分类] 电力

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