Abstract

Suppose that f: ℍ n → ℍ n (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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