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Mat. Sb., 2016, Volume 207, Number 9, Pages 35–56 (Mi msb8598)  

This article is cited in 2 scientific papers (total in 2 papers)

Locally isometric coverings of the Lie group $\mathrm{SO}_0(2,1)$ with special sub-Riemannian metric

V. N. Berestovskiia, I. A. Zubarevab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We find geodesics, shortest arcs, conjugate sets, cut loci, and distances on locally isometric coverings of the Lie group $\mathrm{SO}_0(2,1)$ with a left-invariant sub-Riemannian metric which is right-invariant with respect to the Lie subgroup $1\oplus \mathrm{SO}(2)\subset \mathrm{SO}_0(2,1)$.
Bibliography: 18 titles.

Keywords: geodesic, geodesic orbit space, invariant sub-Riemannian metric, shortest arc, covering space, weakly symmetric space.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.B25.31.0029
НШ-2263.2014.10
Russian Foundation for Basic Research 14-01-00068-a
The work was supported by a grant of the Government of the Russian Federation for the State Support of Scientific Research (agreement no. 14.B25.31.0029), by the Russian Foundation for Basic Research (grant no. 14-01-00068-a) and by the State Programme of the support of leading scientific schools of the Russian Federation (grant no. НШ-2263.2014.10).


DOI: https://doi.org/10.4213/sm8598

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English version:
Sbornik: Mathematics, 2016, 207:9, 1215–1235

Bibliographic databases:

Document Type: Article
UDC: 514.763+512.81+517.911
MSC: Primary 22E30; Secondary 53C17
Received: 07.09.2015 and 11.04.2016

Citation: V. N. Berestovskii, I. A. Zubareva, “Locally isometric coverings of the Lie group $\mathrm{SO}_0(2,1)$ with special sub-Riemannian metric”, Mat. Sb., 207:9 (2016), 35–56; Sb. Math., 207:9 (2016), 1215–1235

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. N. Berestovskii, “Geodesics and curvatures of special sub-Riemannian metrics on Lie groups”, Siberian Math. J., 59:1 (2018), 31–42  mathnet  crossref  crossref  isi  elib
    2. M. V. Tryamkin, “The geodesics of a sub-Riemannian metric on the group of semiaffine transformations of the Euclidean plane”, Siberian Math. J., 60:1 (2019), 164–177  mathnet  crossref  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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