Pseudo-Riemann空间Spm+p中的紧致极大类空子流形

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.