Geodesic
The structure of similarity homogeneous locally compact spaces with an intrinsic metric
Matematičeskie trudy, Tome 17 (2014) no. 2, pp. 132-141

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We study locally compact spaces with an intrinsic metric such that the group of metric similarities is transitive and the group of isometries is not transitive. We confirm Berestovskiǐ's conjecture on the structure of such spaces. 
@article{MT_2014_17_2_a6,
     author = {I. A. Gundyrev},
     title = {The structure of similarity homogeneous locally compact spaces with an intrinsic metric},
     journal = {Matemati\v{c}eskie trudy},
     pages = {132--141},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2014_17_2_a6/}
}
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I. A. Gundyrev. The structure of similarity homogeneous locally compact spaces with an intrinsic metric. Matematičeskie trudy, Tome 17 (2014) no. 2, pp. 132-141. http://geodesic.mathdoc.fr/item/MT_2014_17_2_a6/