摘要
研究了局部对称deSitter空间Nn+11中具有常数量曲率的n维紧致类空超曲面,利用一个自伴随算子及活动标架法得到了这种类空超曲面的刚性分类定理.同时给出了deSitter空间Sn+11中标准数量曲率为常数的n维紧致类空超曲面的相应分类定理,所得结果推广了Zheng和Liu的结果,并使Pinching常数只与维数n有关.
The compact n dimensional space-like hypersurfaces with constant scalar curvature in locally symmetric de Sitter space N^(n+1)_1 are studied, with some rigidity characterization theorems obtained by introducing a self-adjoint operator and by using the moving frame method. As a corollary, the rigidity characterization theorem is obtained on the space-like hypersurfaces in a de Sitter space S^(n+1)_1. These results generalize the results of Zheng and Liu, and the pinching constants do not depend on the dimensional n.
出处
《西安电子科技大学学报》
EI
CAS
CSCD
北大核心
2004年第1期119-123,共5页
Journal of Xidian University
基金
国家自然科学基金资助项目(69972036)
陕西省自然科学基金资助项目(2003A02)
陕西省教育厅自然科学基金资助项目(03JK215)
关键词
局部对称
DE
SITTER空间
类空超曲面
数量曲率
全脐
locally symmetric
de Sitter space
space-like hypersurfaces
totally umbilical
hyperbolic cylinder