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Baokui Li and Yuefei Wang
A new characterization for isometries by triangles
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| Published: |
September 18, 2009 |
| Keywords: |
Isometry, geodesic, affine transformation, triangle preserving, triangle domain preserving |
| Subject: |
30C35, 51F99 |
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Abstract
Let Rn be an n-dimensional Euclidean space and
Dn be an
n-dimensional hyperbolic space with the
Poincaré metric for n>1. In this
paper, we shall prove the following results. (i) A bijection
f:Dn→Dn is an isometry
(Möbius transformation) if and
only if f is triangle preserving. (ii) A bijection
f:Rn→Rn
is an affine transformation if and only if f is triangle
preserving.
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| Acknowledgements
The research was supported by NSFC and MSBRD Program of China
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| 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
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