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

Homogeneous Sub-Riemannian Geodesics on a Group of Motions of the Plane Homogeneous sub-Riemannian geodesics are described for the standard sub-Riemannianstructure on the group \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathrm {SE}}(2)$$\end{document} ofproper motions of the plane. It is shown that this structure is not geodesically orbital, despite theinvariance of the cut time when the initial point is shifted along the geodesics. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

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

, Volume 57 (11) – Nov 1, 2021
5 pages

/lp/springer-journals/homogeneous-sub-riemannian-geodesics-on-a-group-of-motions-of-the-Yq7IuVQoSH
Publisher
Springer Journals
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/s0012266121110148
Publisher site
See Article on Publisher Site

### Abstract

Homogeneous sub-Riemannian geodesics are described for the standard sub-Riemannianstructure on the group \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathrm {SE}}(2)$$\end{document} ofproper motions of the plane. It is shown that this structure is not geodesically orbital, despite theinvariance of the cut time when the initial point is shifted along the geodesics.

### Journal

Differential EquationsSpringer Journals

Published: Nov 1, 2021

### References

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