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Sibirsk. Mat. Zh., 2016, Volume 57, Number 3, Pages 527–542 (Mi smj2762)  

This article is cited in 6 scientific papers (total in 6 papers)

Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group $SL(2)$

V. N. Berestovskiĭa, I. A. Zubarevab

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

Abstract: The authors found geodesics, shortest arcs, cut loci, and conjugate sets for some leftinvariant sub-Riemannian metric on the Lie group $SL(2)$ that is right-invariant relative to the Lie subgroup $SO(2)\subset SL(2)$ (in other words, for invariant sub-Riemannian metric on weakly symmetric space $(SL(2)\times SO(2))/SO(2))$.

Keywords: cut locus, conjugate set, geodesic, geodesic orbit space, Lie algebra, Lie group, invariant sub-Riemannian metric, shortest arc, 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 authors were partially supported by the Russian Foundation for Basic Research (Grant 14-01-00068-a), the Government of the Russian federation for the State Support of Scientific Research (Agreement 14.B25.31.0029), and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-2263.2014.1).


DOI: https://doi.org/10.17377/smzh.2016.57.304

Full text: PDF file (531 kB)
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English version:
Siberian Mathematical Journal, 2016, 57:3, 411–424

Bibliographic databases:

Document Type: Article
UDC: 519.46+514.763+512.81+519.9+517.911
Received: 29.03.2015

Citation: V. N. Berestovskiǐ, I. A. Zubareva, “Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group $SL(2)$”, Sibirsk. Mat. Zh., 57:3 (2016), 527–542; Siberian Math. J., 57:3 (2016), 411–424

Citation in format AMSBIB
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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. Berestovskiǐ, I. A. Zubareva, “Sub-Riemannian distance on the Lie group $SO_0(2,1)$”, St. Petersburg Math. J., 28:4 (2017), 477–489  mathnet  crossref  mathscinet  isi  elib
    2. V. N. Berestovskii, I. A. Zubareva, “Locally isometric coverings of the Lie group $\mathrm{SO}_0(2,1)$ with special sub-Riemannian metric”, Sb. Math., 207:9 (2016), 1215–1235  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. V. N. Berestovskiǐ, I. A. Zubareva, “Sub-Riemannian distance on the Lie group $\operatorname{SL}(2)$”, Siberian Math. J., 58:1 (2017), 16–27  mathnet  crossref  crossref  isi  elib  elib
    4. M. V. Tryamkin, “Geodesics on a group of semi-affine transformations of Euclidean plane”, Russian Math. (Iz. VUZ), 62:7 (2018), 74–77  mathnet  crossref  isi
    5. 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
    6. M. V. Tryamkin, “Geodezicheskie subrimanovoi metriki na gruppe poluaffinnykh preobrazovanii evklidovoi ploskosti”, Sib. matem. zhurn., 60:1 (2019), 214–228  mathnet  crossref
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