Surfaces of genus $g\geq 1$ in 3D contact sub-Riemannian manifolds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909251941695488 |
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| author | Bellini, Eugenio Boscain, Ugo |
| author_facet | Bellini, Eugenio Boscain, Ugo |
| contents | We consider surfaces embedded in a 3D contact sub-Riemannian manifold and the problem of the finiteness of the induced distance (i.e., the infimum of the length of horizontal curves that belong to the surface). Recently it has been proved that for a surface having the topology of a sphere embedded in a tight co-orientable structure, the distance is always finite. In this paper we study closed surfaces of genus larger than 1, proving that such surfaces can be embedded in such a way that the induced distance is finite or infinite. We then study the structural stability of the finiteness/not-finiteness of the distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_03373 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Surfaces of genus $g\geq 1$ in 3D contact sub-Riemannian manifolds Bellini, Eugenio Boscain, Ugo Differential Geometry Dynamical Systems 53D10 / 53C17 / 93B03 We consider surfaces embedded in a 3D contact sub-Riemannian manifold and the problem of the finiteness of the induced distance (i.e., the infimum of the length of horizontal curves that belong to the surface). Recently it has been proved that for a surface having the topology of a sphere embedded in a tight co-orientable structure, the distance is always finite. In this paper we study closed surfaces of genus larger than 1, proving that such surfaces can be embedded in such a way that the induced distance is finite or infinite. We then study the structural stability of the finiteness/not-finiteness of the distance. |
| title | Surfaces of genus $g\geq 1$ in 3D contact sub-Riemannian manifolds |
| topic | Differential Geometry Dynamical Systems 53D10 / 53C17 / 93B03 |
| url | https://arxiv.org/abs/2305.03373 |