A. D. Alexandrov’s problem for non-positively curved spaces in the sense of Busemann
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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.
Key words and phrasesAlexandrov’s problem non-positive curvature geodesic isometry r-sequence geodesic boundary horofunction boundary
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