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Spacelike submanifolds with parallel mean curvature vector in a de Sitter space \(S^{n+p}_{q}(c)\)
Journal of Inequalities and Applications ( IF 1.5 ) Pub Date : 2020-08-12 , DOI: 10.1186/s13660-020-02469-8
Junfeng Chen , Sanyang Liu , Shichang Shu

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.

中文翻译:

de Sitter空间\(S ^ {n + p} _ {q}(c)\)中具有平行平均曲率向量的类空子流形

类空子流形通常出现在与广义相对论的因果关系相关的问题的研究中。在本文中,我们研究了索引为q($ 1 \ leq q的$(n + p)$-维连通de Sitter空间$ S ^ {n + p} _ {q}(c)$$中的n维类空子流形。 \ leq p $)和恒定曲率c,我们得到了Simons型和刚度定理的一些积分不等式。
更新日期:2020-08-14
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