Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.16065 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915023928950784 |
|---|---|
| author | Glutsyuk, A. Sachkov, Yu. |
| author_facet | Glutsyuk, A. Sachkov, Yu. |
| contents | We study the projection of the left-invariant sub-Riemannian structure on the 3D Heisenberg group $G$ to the Heisenberg 3D nil-manifold $M$ -- the compact homogeneous space of $G$ by the discrete Heisenberg group.
First we describe dynamical properties of the geodesic flow for $M$: periodic and dense orbits, and a dynamical characterization of the normal Hamiltonian flow of Pontryagin maximum principle. Then we obtain sharp twoside bounds of sub-Riemannian balls and distance in $G$, and on this basis we estimate the cut time for sub-Riemannian geodesics in $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16065 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sub-Riemannian geodesics on the Heisenberg 3D nil-manifold Glutsyuk, A. Sachkov, Yu. Differential Geometry Dynamical Systems Optimization and Control 53C17, 37C10, 49K15 We study the projection of the left-invariant sub-Riemannian structure on the 3D Heisenberg group $G$ to the Heisenberg 3D nil-manifold $M$ -- the compact homogeneous space of $G$ by the discrete Heisenberg group. First we describe dynamical properties of the geodesic flow for $M$: periodic and dense orbits, and a dynamical characterization of the normal Hamiltonian flow of Pontryagin maximum principle. Then we obtain sharp twoside bounds of sub-Riemannian balls and distance in $G$, and on this basis we estimate the cut time for sub-Riemannian geodesics in $M$. |
| title | Sub-Riemannian geodesics on the Heisenberg 3D nil-manifold |
| topic | Differential Geometry Dynamical Systems Optimization and Control 53C17, 37C10, 49K15 |
| url | https://arxiv.org/abs/2406.16065 |