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Sibirsk. Mat. Zh., 2017, Volume 58, Number 1, Pages 22–35 (Mi smj2836)  

This article is cited in 1 scientific paper (total in 1 paper)

Sub-Riemannian distance on the Lie group $\operatorname{SL}(2)$

V. N. Berestovskiĭa, I. A. Zubarevab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Sobolev Institute of Mathematics, Omsk Branch, Omsk, Russia

Abstract: We find the distances between arbitrary elements of the Lie group $\operatorname{SL}(2)$ for the left invariant sub-Riemannian metric also invariant with respect to the right shifts by elements of the Lie subgroup $\operatorname{SO}(2)\subset\operatorname{SL}(2)$, in other words, the invariant sub-Riemannian metric on the weakly symmetric space $(\operatorname{SL}(2)\times\operatorname{SO}(2))/\operatorname{SO}(2)$ of Selberg.

Keywords: distance, geodesic, geodesic orbit space, Lie algebra, Lie group, invariant sub-Riemannian metric, shortest arc.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.B25.31.0029
Russian Foundation for Basic Research 14-01-00068-a
The authors were supported in part by the Russian Foundation for Basic Research (Grant 14-01-00068-a) and the Government of the Russian Federation for the State Support of Scientific Research (Agreement 14.B25.31.0029).


DOI: https://doi.org/10.17377/smzh.2017.58.103

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English version:
Siberian Mathematical Journal, 2017, 58:1, 16–27

Bibliographic databases:

Document Type: Article
UDC: 519.46+514.763+512.81+519.9+517.911
Received: 25.06.2015

Citation: V. N. Berestovskiǐ, I. A. Zubareva, “Sub-Riemannian distance on the Lie group $\operatorname{SL}(2)$”, Sibirsk. Mat. Zh., 58:1 (2017), 22–35; Siberian Math. J., 58:1 (2017), 16–27

Citation in format AMSBIB
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\by V.~N.~Berestovski{\v\i}, I.~A.~Zubareva
\paper Sub-Riemannian distance on the Lie group~$\operatorname{SL}(2)$
\jour Sibirsk. Mat. Zh.
\yr 2017
\vol 58
\issue 1
\pages 22--35
\mathnet{http://mi.mathnet.ru/smj2836}
\crossref{https://doi.org/10.17377/smzh.2017.58.103}
\elib{http://elibrary.ru/item.asp?id=29159899}
\transl
\jour Siberian Math. J.
\yr 2017
\vol 58
\issue 1
\pages 16--27
\crossref{https://doi.org/10.1134/S0037446617010037}
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\elib{http://elibrary.ru/item.asp?id=29485431}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85014663940}


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    Citing articles on Google Scholar: Russian citations, English citations
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    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
  • Сибирский математический журнал Siberian Mathematical Journal
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