 

Baokui Li and Yuefei Wang
A new characterization for isometries by triangles


Published: 
September 18, 2009 
Keywords: 
Isometry, geodesic, affine transformation, triangle preserving, triangle domain preserving 
Subject: 
30C35, 51F99 


Abstract
Let R^{n} be an ndimensional Euclidean space and
D^{n} be an
ndimensional hyperbolic space with the
Poincaré metric for n>1. In this
paper, we shall prove the following results. (i) A bijection
f:D^{n}→D^{n} is an isometry
(Möbius transformation) if and
only if f is triangle preserving. (ii) A bijection
f:R^{n}→R^{n}
is an affine transformation if and only if f is triangle
preserving.


Acknowledgements
The research was supported by NSFC and MSBRD Program of China


Author information
Baokui Li:
Department of Mathematics, Beijing Institute of Technology, 100081, China
henan_lbk@bit.edu.cn
Yuefei Wang:
Institute of Mathematics, AMSS, Chinese Academy of Sciences, 100190, China
wangyf@math.ac.cn

