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Izv. Vyssh. Uchebn. Zaved. Mat., 2010, Number 9, Pages 10–35 (Mi ivm7125)  

This article is cited in 2 scientific papers (total in 2 papers)

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

P. D. Andreev

Chair of Algebra and Geometry, Pomorskii State University, Arkhandel'sk, Russia

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 characterizied as follows: if a bijection $f\colon X\to X$ and its inverse $f^{-1}$ preserve distance 1, then $f$ is an isometry.

Keywords: Alexandrov's problem, non-positive curvature, geodesic, isometry, $r$-sequence, geodesic boundary, horofunction boundary.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:9, 7–29

Bibliographic databases:

Document Type: Article
UDC: 514.774
Received: 01.12.2008

Citation: P. D. Andreev, “A. D. Alexandrov's problem for non-positively curved spaces in the sense of Busemann”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 9, 10–35; Russian Math. (Iz. VUZ), 54:9 (2010), 7–29

Citation in format AMSBIB
\Bibitem{And10}
\by P.~D.~Andreev
\paper A.\,D.~Alexandrov's problem for non-positively curved spaces in the sense of Busemann
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 9
\pages 10--35
\mathnet{http://mi.mathnet.ru/ivm7125}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2789304}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 9
\pages 7--29
\crossref{https://doi.org/10.3103/S1066369X10090021}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649602863}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. P. D. Andreev, “The proof of Busemann conjecture for $G$-spaces with non-positive curvature”, St. Petersburg Math. J., 26:2 (2015), 193–206  mathnet  crossref  mathscinet  isi  elib
    2. P. D. Andreev, “Normed Space Structure on a Busemann $G$-Space of Cone Type”, Math. Notes, 101:2 (2017), 193–202  mathnet  crossref  crossref  mathscinet  isi  elib
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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