Compact Maximal Space-like Submanifolds in a Pseudo-Riemannian Spacetime Sp^m＋p

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.     

anti-de Sitter 空间中紧致类空超曲面的积分公式及其在常高阶平均曲率下的应用

该文对 anti-de Sitter 空间H₁ⁿ⁺¹中的紧致类空超曲面建立了积分公式,并应用它们在常高阶平均曲率的条件下讨论了H₁ⁿ⁺¹中紧致类空超曲面的全脐问题.     

何时任意常半径的切球丛是Einstein的

研究具有任意常半径r的切球丛,得到该切球丛是Einstein的一个充分必要条件。     

小Excess与具负下界Ricci曲率开流形的拓扑

In this paper,we study the relation between the excess of open manifolds and their topology by using the methods of comparison geometry.We prove that a complete open Riemmannian manifold with Ricci curvature negatively lower bounded is of finite topological type provided that the conjugate radius is bounded from below by a positive constant and its Excess is bounded by some function of its conjugate radius,which improves some results in [4].