| de Sitter空间S1m+1中具有平行Blaschke张量的正则类空超曲面 |
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| 引用本文： | 李兴校,宋虹儒.de Sitter空间S1m+1中具有平行Blaschke张量的正则类空超曲面[J].数学杂志,2016,36(6):1183-1200. |
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| 作者姓名： | 李兴校 宋虹儒 |
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| 作者单位： | 河南师范大学数学与信息科学学院, 河南 新乡 453007,河南师范大学数学与信息科学学院, 河南 新乡 453007 |
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| 基金项目： | Supported by National Natural Science Foundation of China (11171091; 11371018). |
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| 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.
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| 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 |
| 收稿时间： | 2015/7/4 0:00:00 |
| 修稿时间： | 2016/2/19 0:00:00 |
REGULAR SPACE-LIKE HYPERSURFACES IN THE DE SITTER SPACE S1M+1 WITH PARALLEL BLASCHKE TENSORS |
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| LI Xing-xiao and SONG Hong-ru.REGULAR SPACE-LIKE HYPERSURFACES IN THE DE SITTER SPACE S1M+1 WITH PARALLEL BLASCHKE TENSORS[J].Journal of Mathematics,2016,36(6):1183-1200. |
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| Authors: | LI Xing-xiao and SONG Hong-ru |
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| Institution: | School of Mathematics and Science Information, Henan Normal University, Xinxiang 453007, China and 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. |
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| Keywords: | conformal form parallel Blaschke tensor conformal metric conformal second fundamental form maximal hypersurfaces constant scalar curvature |
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