Isometries in hyperbolic spaces  

作　　者：HUANG ManZi WANG XianTao WANG YueFei 

机构地区：[1]Department of Mathematics,Hunan Normal University,Changsha 410081,China [2]Hua Loo-Keng Key Laboratory of Mathematics,Academy of Mathematics and System Science,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Science China Mathematics》2010年第1期71-86,共16页中国科学：数学（英文版）

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

摘　　要：Suppose that f:Hn → Hn (n≥2) maps any r-dimensional hyperplane (1≤r【n) 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.Suppose that f:Hn → Hn (n≥2) maps any r-dimensional hyperplane (1≤r<n) 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.

关 键 词：surjective MAP GEODESIC HYPERPLANE ISOMETRY M¨obius TRANSFORMATION 

分 类 号：N[自然科学总论]