Finite Homogeneous Metric Spaces
- Authors: Berestovskii V.N.1,2, Nikonorov Y.G.3
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Affiliations:
- Sobolev Institute of Mathematics
- Novosibirsk State University
- Southern Mathematical Institute
- Issue: Vol 60, No 5 (2019)
- Pages: 757-773
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172616
- DOI: https://doi.org/10.1134/S0037446619050021
- ID: 172616
Cite item
Abstract
The authors study the class of finite homogeneous metric spaces and some of its important subclasses that have natural definitions in terms of the metrics and well-studied analogs in the class of Riemannian manifolds. The relationships between these classes are explored. The examples of the corresponding spaces are built, some of which are the vertex sets of the special convex polytopes in Euclidean space. We describe the classes on using the language of graph theory, which enables us to provide some examples of finite metric spaces with unusual properties. Several unsolved problems are posed.
About the authors
V. N. Berestovskii
Sobolev Institute of Mathematics; Novosibirsk State University
Author for correspondence.
Email: vberestov@inbox.ru
Russian Federation, 4 Koptuyg Av., Novosibirsk, 630090; 1 Pirogov Str., Novosibirsk, 630090
Yu. G. Nikonorov
Southern Mathematical Institute
Author for correspondence.
Email: nikonorov2006@mail.ru
Russian Federation, 22 Markus Str., Vladikavkaz, 362027
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