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Sibirskii Matematicheskii Zhurnal, 2023, Volume 64, Number 3, Pages 521–539
DOI: https://doi.org/10.33048/smzh.2023.64.306 (Mi smj7778) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Geodesics and shortest arcs of some sub-Riemannian metrics on the Lie groups $SU(2)\times{\Bbb R}$ and $SO(3)\times{\Bbb R}$ with three-dimensional generating distributions

I. A. Zubareva

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
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DOI: https://doi.org/10.33048/smzh.2023.64.306
Abstract: We find geodesics, shortest arcs, cut loci, first conjugate loci, and distances between arbitrary elements for some left-invariant sub-Riemannian metrics on the Lie groups $SU(2)\times{\Bbb R}$ and $SO(3)\times{\Bbb R}$.
Keywords: geodesic, left-invariant sub-Riemannian metric, Lie algebra, Lie group, shortest arc, cut locus, first conjugate locus.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0003
The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0003).
Received: 09.11.2022
Revised: 09.11.2022
Accepted: 21.02.2023
English version:
Siberian Mathematical Journal, 2023, Volume 64, Issue 3, Pages 575–592
DOI: https://doi.org/10.1134/S0037446623030060
Document Type: Article
UDC: 514.752.8+514.763+514.765+514.764.227
MSC: 35R30
Language: Russian
Citation: I. A. Zubareva, “Geodesics and shortest arcs of some sub-Riemannian metrics on the Lie groups $SU(2)\times{\Bbb R}$ and $SO(3)\times{\Bbb R}$ with three-dimensional generating distributions”, Sibirsk. Mat. Zh., 64:3 (2023), 521–539; Siberian Math. J., 64:3 (2023), 575–592
Citation in format AMSBIB
\Bibitem{Zub23}
\by I.~A.~Zubareva
\paper Geodesics and shortest arcs of some sub-Riemannian metrics on the Lie groups $SU(2)\times{\Bbb R}$ and~$SO(3)\times{\Bbb R}$ with three-dimensional generating distributions
\jour Sibirsk. Mat. Zh.
\yr 2023
\vol 64
\issue 3
\pages 521--539
\mathnet{http://mi.mathnet.ru/smj7778}
\transl
\jour Siberian Math. J.
\yr 2023
\vol 64
\issue 3
\pages 575--592
\crossref{https://doi.org/10.1134/S0037446623030060}
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