de Sitter空间Sm+11中具有平行Blaschke张量的正则类空超曲面

摘要

In this paper, we introduce two conformal non-homogeneous coordinate systems. Modeled on the de Sitter space Sm+11 , we cover the conformal space Qm+11 . The conformal geometry of regular space-like hypersurfaces in Qm+11 can be treated as in the M¨obius geometry of hyper-surfaces in the sphere Sm+1. As a result, we give a complete classification of the regular space-like hypersurfaces with parallel Blaschke tensors.%本文引入两个以de Sitter空间为模型的非齐性坐标来覆盖共形空间Qm+11.利用球面Sm+1中超曲面的M¨obius 几何的方法，本文研究了Qm+11中正则类空超曲面的共形几何.作为其结果，本文对所有具有平行Blaschke张量的正则类空超曲面进行了完全分类.