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Sibirsk. Mat. Zh., 2010, Volume 51, Number 6, Pages 1215–1227 (Mi smj2156)  

Solution of a Busemann problem

V. N. Berestovskiĭ

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science, Omsk

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.

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English version:
Siberian Mathematical Journal, 2010, 51:6, 962–970

Bibliographic databases:

Document Type: Article
UDC: 513.813+519.46
Received: 15.10.2009

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

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