Metric Lines in the Special Euclidean group on the plane
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866913599372394496 |
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| author | Wang, Y. Ku, S. Bravo-Doddoli, A. |
| author_facet | Wang, Y. Ku, S. Bravo-Doddoli, A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13873 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Metric Lines in the Special Euclidean group on the plane Wang, Y. Ku, S. Bravo-Doddoli, A. Differential Geometry 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. |
| title | Metric Lines in the Special Euclidean group on the plane |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2408.13873 |