de Sitter空间S_1^(m+1)中具有平行Blaschke张量的正则类空超曲面（英文）  

REGULAR SPACE-LIKE HYPERSURFACES IN THE DE SITTER SPACE S_1^(M+1) WITH PARALLEL BLASCHKE TENSORS

作　　者：李兴校[1] 宋虹儒 LI Xing-xiao SONG Hong-ru(School of Mathematics and Science Information, Henan Normal University, Xinxiang 453007, Chin)

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453007

出　　处：《数学杂志》2016年第6期1183-1200,共18页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(11171091;11371018)

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Q_1^(m+1).利用球面S^(m+1)中超曲面的M?bius几何的方法,本文研究了Q_1^(m+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.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 Mobius geometry of hypersurfaces in the sphere Sm＋1.As a result,we give a complete classification of the regular space-like hypersurfaces with parallel Blaschke tensors.

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 

分 类 号：O186[理学—数学]