RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. Vyssh. Uchebn. Zaved. Mat.: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (415 kB)
References: PDF file   HTML file

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

Bibliographic databases:

Document Type: Article
UDC: 514.774

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} 

• http://mi.mathnet.ru/eng/ivm7125
• http://mi.mathnet.ru/eng/ivm/y2010/i9/p10

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
2. P. D. Andreev, “Normed Space Structure on a Busemann $G$-Space of Cone Type”, Math. Notes, 101:2 (2017), 193–202
•  Number of views: This page: 241 Full text: 51 References: 17 First page: 5