Isometries in hyperbolic spaces

作     者：HUANG ManZi WANG XianTao WANG YueFei 

作者机构：Department of MathematicsHunan Normal UniversityChangsha 410081China Hua Loo-Keng Key Laboratory of MathematicsAcademy of Mathematics and System ScienceChinese Academy of SciencesBeijing 100190China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2010年第53卷第1期

页      面：71-86页

核心收录：

学科分类：07[理学] 08[工学] 

基　　金：supported by National Natural Science Foundation of China (Grant No.10771059) Tianyuan Foundation 

主　　题：surjective map geodesic hyperplane isometry M¨obius transformation 

摘      要：Suppose that f:Hn → Hn (n≥2) maps any r-dimensional hyperplane (1≤rn) into an r-dimensional hyperplane. In this paper, we prove that f is an isometry if and only if f is a surjective map. This result gives an affirmative answer to a recent conjecture due to Li and Yao.