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 ].
出处
《黑龙江大学自然科学学报》
CAS
北大核心
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)
关键词
非拟退化映射
满射
NP条件
F条件
等距
Mcibius变换
non-pseudo-degenerate map
surjective map
NP-condition
F-condition
isometry
Mobius transformation
