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A. D. Alexandrov’s problem for non-positively curved spaces in the sense of Busemann

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Abstract

This paper is the last of a series devoted to the solution of Alexandrov’s problem for non-positively curved spaces. Here we study non-positively curved spaces in the sense of Busemann. We prove that isometries of a geodesically complete connected at infinity proper Busemann space X are characterized as follows: If a bijection f: X → X and its inverse f −1 preserve distance 1, then f is an isometry.

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Authors and Affiliations

  1. Pomor State University, pr. Lomonosova 4, Arkhangelsk, 163002, Russia

    P. D. Andreev

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  1. P. D. Andreev
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Correspondence to P. D. Andreev.

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Original Russian Text © P.D. Andreev, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 9, pp. 10–35.

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Andreev, P.D. A. D. Alexandrov’s problem for non-positively curved spaces in the sense of Busemann. Russ Math. 54, 7–29 (2010). https://doi.org/10.3103/S1066369X10090021

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