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Homogeneous Sub-Riemannian Geodesics on a Group of Motions of the Plane

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Abstract

Homogeneous sub-Riemannian geodesics are described for the standard sub-Riemannian structure on the group \({\mathrm {SE}}(2)\) of proper motions of the plane. It is shown that this structure is not geodesically orbital, despite the invariance of the cut time when the initial point is shifted along the geodesics.

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ACKNOWLEDGMENTS

The author is grateful to A.V. Podobryaev for useful discussions of this work, as well as the referee for valuable information on publications on the topic of the article.

Funding

This work was supported by the Russian Science Foundation, project no. 17-11-01387-P.

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Authors and Affiliations

  1. Program Systems Institute, Russian Academy of Sciences, Pereslavl-Zalessky, Yaroslavl oblast, 152020, Russia

    Yu. L. Sachkov

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  1. Yu. L. Sachkov
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Correspondence to Yu. L. Sachkov.

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Translated by V. Potapchouck

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Sachkov, Y.L. Homogeneous Sub-Riemannian Geodesics on a Group of Motions of the Plane. Diff Equat 57, 1550–1554 (2021). https://doi.org/10.1134/S0012266121110148

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  • DOI: https://doi.org/10.1134/S0012266121110148

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