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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 6, Pages 1215–1227 (Mi smj2156)  
This article is cited in 2 scientific papers (total in 2 papers)

Solution of a Busemann problem

V. N. Berestovskiĭ

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science, Omsk
Full-text PDF (348 kB) Citations (2)
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Abstract: We give a solution to the problem posed by Busemann which is as follows: Determine the noncompact Busemann $G$-spaces such that for every two geodesics there exists a motion taking one to the other. We prove that each of these spaces is isometric to the Euclidean space or to one of the noncompact symmetric spaces of rank 1 (of negative sectional curvature).
Keywords: Busemann $G$-space, geodesic, aspheric homogeneous Riemannian manifold, Lie group with a left-invariant metric, geodesic orbit space, isotropic homogeneous Riemannian manifold, Euclidean space, symmetric Riemannian space of rank 1.
Received: 15.10.2009
English version:
Siberian Mathematical Journal, 2010, Volume 51, Issue 6, Pages 962–970
DOI: https://doi.org/10.1007/s11202-010-0095-3
Bibliographic databases:
Document Type: Article
UDC: 513.813+519.46
Language: Russian
Citation: V. N. Berestovskiǐ, “Solution of a Busemann problem”, Sibirsk. Mat. Zh., 51:6 (2010), 1215–1227; Siberian Math. J., 51:6 (2010), 962–970
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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    References:77
    First page:2
     
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