Metabelian distributions and sub-Riemannian geodesics
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909209861292032 |
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| author | Donne, Enrico Le Paddeu, Nicola Socionovo, Alessandro |
| author_facet | Donne, Enrico Le Paddeu, Nicola Socionovo, Alessandro |
| contents | We begin by characterizing metabelian distributions in terms of principal bundle structures. Then, we prove that in sub-Riemannian manifolds with metabelian distributions of rank $r$, the projection of strictly singular trajectories to some $r$-dimensional manifold must remain within an analytic variety. As a consequence, for rank-2 metabelian distributions, geodesics are of class $C^1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14997 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Metabelian distributions and sub-Riemannian geodesics Donne, Enrico Le Paddeu, Nicola Socionovo, Alessandro Differential Geometry Optimization and Control We begin by characterizing metabelian distributions in terms of principal bundle structures. Then, we prove that in sub-Riemannian manifolds with metabelian distributions of rank $r$, the projection of strictly singular trajectories to some $r$-dimensional manifold must remain within an analytic variety. As a consequence, for rank-2 metabelian distributions, geodesics are of class $C^1$. |
| title | Metabelian distributions and sub-Riemannian geodesics |
| topic | Differential Geometry Optimization and Control |
| url | https://arxiv.org/abs/2405.14997 |