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Mat. Tr., 2012, Volume 15, Number 1, Pages 120–128 (Mi mt230)  

This article is cited in 3 scientific papers (total in 3 papers)

The geodesic flow of a sub-Riemannian metric on a solvable lie group

A. D. Mazhitova

Al Farabi Kazakh State University, Almaty, Kazakhstan

Abstract: We consider the sub-Riemannian problem on the three-dimensional solvable Lie group $\mathrm{SOLV}^+$. The problem is based on constructing a Hamiltonian structure for a given metric by the Pontryagin Maximum Principle.

Key words: sub-Riemannian geometry, left-invariant metric, Hamiltonian, geodesics.

Full text: PDF file (187 kB)
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English version:
Siberian Advances in Mathematics, 2013, 23:2, 99–105

Bibliographic databases:

Document Type: Article
UDC: 514.7
Received: 23.08.2011

Citation: A. D. Mazhitova, “The geodesic flow of a sub-Riemannian metric on a solvable lie group”, Mat. Tr., 15:1 (2012), 120–128; Siberian Adv. Math., 23:2 (2013), 99–105

Citation in format AMSBIB
\Bibitem{Maz12}
\by A.~D.~Mazhitova
\paper The geodesic flow of a~sub-Riemannian metric on a~solvable lie group
\jour Mat. Tr.
\yr 2012
\vol 15
\issue 1
\pages 120--128
\mathnet{http://mi.mathnet.ru/mt230}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2984679}
\elib{http://elibrary.ru/item.asp?id=17718101}
\transl
\jour Siberian Adv. Math.
\yr 2013
\vol 23
\issue 2
\pages 99--105
\crossref{https://doi.org/10.3103/S1055134413020041}


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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. A. D. Mazhitova, “The normal sub-Riemannian geodesic flow on $E(2)$ generated by a left-invariant metric and a right-invariant distribution”, Siberian Math. J., 55:5 (2014), 948–953  mathnet  crossref  mathscinet  isi
    2. S. V. Agapov, “On the sub-Riemannian geodesic flow for the Goursat distribution”, Siberian Math. J., 57:1 (2016), 1–6  mathnet  crossref  crossref  mathscinet  isi  elib
    3. S. V. Agapov, M. R. Borchashvili, “On a certain sub-Riemannian geodesic flow on the Heisenberg group”, Siberian Math. J., 58:6 (2017), 943–951  mathnet  crossref  crossref  isi  elib
  • Математические труды Siberian Advances in Mathematics
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