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Sibirsk. Mat. Zh., 2019, Volume 60, Number 1, Pages 214–228 (Mi smj3071)  

The geodesics of a sub-Riemannian metric on the group of semiaffine transformations of the Euclidean plane

M. V. Tryamkinab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: We obtain the parametrized representations of the geodesics of a left-invariant sub-Riemannian metric on the group of semiaffine transformations of the Euclidean plane. These transformations act as orientation-preserving affine mappings along one axis and as translations along the other.

Keywords: geodesic, sub-Riemannian structure, Lie group.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00801_а
The author was supported by the Russian Foundation for Basic Research (Grant 17-01-00801a).


DOI: https://doi.org/10.33048/smzh.2019.60.118

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English version:
Siberian Mathematical Journal, 2019, 60:1, 164–177

Bibliographic databases:

Document Type: Article
UDC: 514.7
Received: 03.05.2018
Revised: 10.08.2018
Accepted:17.10.2018

Citation: M. V. Tryamkin, “The geodesics of a sub-Riemannian metric on the group of semiaffine transformations of the Euclidean plane”, Sibirsk. Mat. Zh., 60:1 (2019), 214–228; Siberian Math. J., 60:1 (2019), 164–177

Citation in format AMSBIB
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\paper The geodesics of a sub-Riemannian metric on the group of semiaffine transformations of the Euclidean plane
\jour Sibirsk. Mat. Zh.
\yr 2019
\vol 60
\issue 1
\pages 214--228
\mathnet{http://mi.mathnet.ru/smj3071}
\crossref{https://doi.org/10.33048/smzh.2019.60.118}
\transl
\jour Siberian Math. J.
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\vol 60
\issue 1
\pages 164--177
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