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Solution of a Busemann problem

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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).

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Authors and Affiliations

  1. Omsk Branch of the Sobolev Institute of Mathematics, Omsk, Russia

    V.N. Berestovskii

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  1. V.N. Berestovskii
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Correspondence to V.N. Berestovskii.

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Original Russian Text Copyright © 2010 Berestovskii V. N.

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Berestovskii, V. Solution of a Busemann problem. Sib Math J 51, 962–970 (2010). https://doi.org/10.1007/s11202-010-0095-3

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  • DOI: https://doi.org/10.1007/s11202-010-0095-3

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