Novel pathways in $k$-contact geometry
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909626057883648 |
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| author | Sobczak, Tomasz Frelik, Tymon |
| author_facet | Sobczak, Tomasz Frelik, Tymon |
| contents | Our study of Goursat distributions originates new types of $k$-contact distributions and Lie systems with applications. In particular, families of generators for Goursat distributions on $\mathbb{R}^4, \mathbb{R}^5$ and $\mathbb{R}^6$ give rise to Lie systems and we characterise Goursat structures that are $k$-contact distributions. Our results are used to study the zero-trailer and other systems via Lie systems and $k$-contact manifolds. New ideas for the development of superposition rules via geometric structures and the characterisation of $k$-contact distributions are given and applied. Some relations of $k$-contact geometry with parabolic Cartan geometries are inspected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22294 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Novel pathways in $k$-contact geometry Sobczak, Tomasz Frelik, Tymon Differential Geometry Exactly Solvable and Integrable Systems Our study of Goursat distributions originates new types of $k$-contact distributions and Lie systems with applications. In particular, families of generators for Goursat distributions on $\mathbb{R}^4, \mathbb{R}^5$ and $\mathbb{R}^6$ give rise to Lie systems and we characterise Goursat structures that are $k$-contact distributions. Our results are used to study the zero-trailer and other systems via Lie systems and $k$-contact manifolds. New ideas for the development of superposition rules via geometric structures and the characterisation of $k$-contact distributions are given and applied. Some relations of $k$-contact geometry with parabolic Cartan geometries are inspected. |
| title | Novel pathways in $k$-contact geometry |
| topic | Differential Geometry Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2505.22294 |