局部对称de Sitter空间中的紧致类空超曲面

Compact space-like hypersurfaces with constant scalar curvaturein locally symmetric de Sitter space

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.