This article is cited in 2 papers

Similarly homogeneous locally compact spaces with an intrinsic measure

I. A. Gundyrev

Omsk State University

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 д-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.

Keywords: similarity homogeneous space, intrinsic metric, submetry, space of curvature bounded below in the sense of A. D. Aleksandrov, homogeneous space, $\delta$-homogeneous space.

UDC: 517.982:513.813

Received: 04.04.2007

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2008, 52:4, 24–37

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