The CR geometry of the three-segment snake
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914813278420992 |
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| author | Frelik, Tymon |
| author_facet | Frelik, Tymon |
| contents | We study the geometry associated with the kinematics of a planar robot known as the "three-segment snake," whose velocity distribution belongs to a class of (2,3,5) distributions. We discover that, under certain assumptions on its construction parameters, the snake may be endowed with a CR structure of CR dimension 1 and real codimension 3. We solve the associated Cartan equivalence problem and find the invariants of the snake's CR structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16898 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The CR geometry of the three-segment snake Frelik, Tymon Differential Geometry We study the geometry associated with the kinematics of a planar robot known as the "three-segment snake," whose velocity distribution belongs to a class of (2,3,5) distributions. We discover that, under certain assumptions on its construction parameters, the snake may be endowed with a CR structure of CR dimension 1 and real codimension 3. We solve the associated Cartan equivalence problem and find the invariants of the snake's CR structure. |
| title | The CR geometry of the three-segment snake |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2405.16898 |