Sub-Riemannian optimal synthesis for Carnot groups with the structure of a path geometry
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917628929376256 |
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| author | Návrat, Aleš Zalabová, Lenka |
| author_facet | Návrat, Aleš Zalabová, Lenka |
| contents | This paper explicitly constructs the complete set of optimal sub-Riemannian geodesics starting from a point for certain Carnot groups of step two. These are groups of dimension 2n+1 equipped with a left-invariant distribution of dimension n+1 such that at each point, there is a unique direction defining a nontrivial Lie bracket. A suitable explicit expression of geodesics, together with symmetries of the structure, allows us to identify the cut time and the cut locus by applying the so-called extended Hadamard technique. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_01831 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sub-Riemannian optimal synthesis for Carnot groups with the structure of a path geometry Návrat, Aleš Zalabová, Lenka Differential Geometry 53C17, 22E60, 35R03 This paper explicitly constructs the complete set of optimal sub-Riemannian geodesics starting from a point for certain Carnot groups of step two. These are groups of dimension 2n+1 equipped with a left-invariant distribution of dimension n+1 such that at each point, there is a unique direction defining a nontrivial Lie bracket. A suitable explicit expression of geodesics, together with symmetries of the structure, allows us to identify the cut time and the cut locus by applying the so-called extended Hadamard technique. |
| title | Sub-Riemannian optimal synthesis for Carnot groups with the structure of a path geometry |
| topic | Differential Geometry 53C17, 22E60, 35R03 |
| url | https://arxiv.org/abs/2404.01831 |