Similarly homogeneous locally compact spaces with an intrinsic measure

I. A. Gundyrev

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2008), pp. 28-42

Résumé

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.

Détail

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