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Isometries in hyperbolic spaces

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Hunan Normal University, Changsha, 410081, China

    ManZi Huang & XianTao Wang

  2. Hua Loo-Keng Key Laboratory of Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing, 100190, China

    YueFei Wang

Authors
  1. ManZi Huang
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  2. XianTao Wang
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  3. YueFei Wang
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Corresponding author

Correspondence to ManZi Huang.

Additional information

This work was supported by National Natural Science Foundation of China (Grant No. 10771059) and Tianyuan Foundation.

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Huang, M., Wang, X. & Wang, Y. Isometries in hyperbolic spaces. Sci. China Ser. A-Math. 53, 71–86 (2010). https://doi.org/10.1007/s11425-010-0005-y

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  • DOI: https://doi.org/10.1007/s11425-010-0005-y

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