欧氏几何下的Mbius变换和双曲几何下的等距(英文)  

Mbius transformations in Euclidean geometry and isometries in hyperbolic geometry

作　　者：李浏兰[1] 

机构地区：[1]衡阳师范学院数学系,衡阳421008

出　　处：《黑龙江大学自然科学学报》2009年第4期436-442,共7页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the Natural Science Foundations of China(10771059);Natural Science Foundations of Hunan Province(05JJ10001);Program for New Century Excellent Talents in University(04-0783);Program for Hengyang Normal University(08B06)

摘　　要：假定f(Hn→Hn)(n≥2)把Hn中的任一r(1≤r<n)维双曲平面映入一个r维双曲平面。如果f是一个非拟退化的满映射且满足NP条件,将证明f是一个双曲等距。对于欧氏几何的情形,也有对应的结果。这些结果部分地回答了李保奎和姚国武在[7]中提出的猜测。Suppose that f：H^n→H^n （n ≥2 ）maps any r-hyperplane （1 ≤ r 〈 n）in H^n into an r-hyperplane in H^n. It is shown that f is an isometry iff is surjective and non-pseudo-degenerate, and satisfies NP-condition. The version for the Euclidean case is also obtained. These results are partial answers to the conjectures raised by Li and Yao recently in [ 7 ].

关 键 词：非拟退化映射 满射 NP条件 F条件 等距 Mcibius变换 

分 类 号：O174.51[理学—数学]