Compact Maximal Space-like Submanifolds in a Pseudo-Riemannian Spacetime S_p^(m+p)

摘要

This paper concerns space-like submanifolds in a pseudo-Riemannian space-time Spm+p(?)Epm+p+1(p≥1), and proves that connected compact maximal space-like submanifolds in a pseudo-Riemannian spacetime Spm+p(?)Epm+p+1(p≥1) must be totally umbilical, and also totally geodesic. Particularly, when p = 1, our result is just Montiel's in case of H = 0.