Metric lines in the special Euclidean group on the plane
Abstract
The Special Euclidean group on the plane $SE(2)$ has the left-invariant sub-Riemannian structure. Every sub-Riemannian manifold possesses a Hamiltonian function governing the sub-Riemannian geodesic flow. Two natural questions are: What are the necessary conditions for periodic sub-Riemannian geodesics? What geodesics are the metric lines in SE(2)? We answer both questions, and our method for the second is an alternative proof using the Hamilton-Jacobi theory.
Fields of Study & Subjects
Mathematics and Applications
Advanced Theoretical and Applied Studies in Material Sciences and Geometry
Computational Geometry and Mesh Generation
Publication details
- Journal / source
- Involve a Journal of Mathematics
- Volume
- 19
- Issue
- 3
- Pages
- 471–490
- Publication date
- 12 June 2026
- Language
- EN