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Sibirskii Matematicheskii Zhurnal, 2017, Volume 58, Number 1, Pages 22–35
DOI: https://doi.org/10.17377/smzh.2017.58.103 (Mi smj2836) 		 
This article is cited in 8 scientific papers (total in 8 papers)

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
Full-text PDF (317 kB) Citations (8)
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DOI: https://doi.org/10.17377/smzh.2017.58.103
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).
Received: 25.06.2015
English version:
Siberian Mathematical Journal, 2017, Volume 58, Issue 1, Pages 16–27
DOI: https://doi.org/10.1134/S0037446617010037
Bibliographic databases:
Document Type: Article
UDC: 519.46+514.763+512.81+519.9+517.911
Language: Russian
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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    • This publication is cited in the following 8 articles:
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    		Сибирский математический журнал Siberian Mathematical Journal
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