| 摘要: |
| 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Q1m+1.利用球面Sm+1中超曲面的Möbius几何的方法,本文研究了Q1m+1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. |
| 关键词: 共形形式 平行Blaschke张量 共形度量 共形第二基本形式 极大超曲面 常数量曲率 |
| DOI： |
| 分类号:O186 |
| 基金项目:Supported by National Natural Science Foundation of China (11171091; 11371018). |
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| REGULAR SPACE-LIKE HYPERSURFACES IN THE DE SITTER SPACE S1M+1 WITH PARALLEL BLASCHKE TENSORS |
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LI Xing-xiao, SONG Hong-ru
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School of Mathematics and Science Information, Henan Normal University, Xinxiang 453007, China
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| Abstract: |
| In this paper, we introduce two conformal non-homogeneous coordinate systems. Modeled on the de Sitter space S1m+1, we cover the conformal space Q1m+1. The conformal geometry of regular space-like hypersurfaces in Q1m+1 can be treated as in the Möbius geometry of hypersurfaces in the sphere Sm+1. As a result, we give a complete classiflcation of the regular space-like hypersurfaces with parallel Blaschke tensors. |
| Key words: conformal form parallel Blaschke tensor conformal metric conformal second fundamental form maximal hypersurfaces constant scalar curvature |
