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Russian Mathematics

, Volume 54, Issue 9, pp 7–29 | Cite as

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

  • P. D. Andreev
Article
  • 34 Downloads

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: XX and its inverse f −1 preserve distance 1, then f is an isometry.

Key words and phrases

Alexandrov’s problem non-positive curvature geodesic isometry r-sequence geodesic boundary horofunction boundary 

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Copyright information

© Allerton Press, Inc. 2010

Authors and Affiliations

  1. 1.Pomor State UniversityArkhangelskRussia

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