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

Abstract

Abstract 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 ) $(n + p)$ -dimensional connected de Sitter space S q n + p ( c ) $S^{n+p}_{q}(c)$ of index q ( 1 ≤ q ≤ p $1\leq q \leq p$ ) and of constant curvature c, and we obtain some integral inequalities of Simons type and rigidity theorems.

Keywords

• De Sitter space
• Spacelike submanifold
• Totally umbilical
• Rigidity theorems