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On similarity homogeneous locally compact spaces with intrinsic metric

Authors
  • Gundyrev, I. A.1
  • 1 Omsk State University named after F. M. Dostoyevskii, prosp. Mira 55a, Omsk, 644077, Russia , Omsk (Russia)
Type
Published Article
Journal
Russian Mathematics
Publisher
Allerton Press, Inc.
Publication Date
Apr 01, 2008
Volume
52
Issue
4
Pages
24–37
Identifiers
DOI: 10.3103/S1066369X0804004X
Source
Springer Nature
Keywords
License
Yellow

Abstract

In this article, we generalize partially the theorem of V. N. Berestovskii on characterization of similarity homogeneous (nonhomogeneous) Riemannian manifolds, i.e., Riemannian manifolds admitting transitive group of metric similarities other than motions to the case of locally compact similarity homogeneous (nonhomogeneous) spaces with intrinsic metric satisfying the additional assumption that the canonically conformally equivalent homogeneous space is δ-homogeneous or a space of curvature bounded below in the sense of A. D. Aleksandrov. Under the same assumptions, we prove the conjecture of V. N. Berestovskii on topological structure of such spaces.

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