On similarity homogeneous locally compact spaces with intrinsic metric (Q1006956)

This paper deals with non-homogeneous similarly homogeneous locally compact spaces with an intrinsic metric. These are metric spaces which admit a transitive (locally compact) group of metric similarities, say \(G\). The main result concerns such a space \((X, \rho)\) with bounded Aleksandrov curvature, or \(\delta\)-homogeneity instead. A description of \(G\) as being isomorphic to a semi-direct product of \((\mathbb R, +)\) and \(I\), the subgroup of isometries, and of \(X\) as \(X\cong G/ H\), where \(H \subset I\), is given. Thus some partial results of \textit{V. N. Berestovskii} [Izv. Vyssh. Uchebn. Zaved. Mat., No.~11, 3--22, Russian Mathematics (Iz. VUZ) 48 (11), 1--19 (2004)] on the subject are extended. The paper concludes with a proof of a conjecture of the latters on the topological structure of the spaces named in the title.