Cone structures and path geometries with constant torsion
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911105573453824 |
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| author | Kryński, Wojciech |
| author_facet | Kryński, Wojciech |
| contents | We study three-dimensional path geometries with nontrivial torsion of maximal rank. We introduce the notion of constant torsion and show that such path geometries are in one-to-one correspondence with certain cone structures modeled on homogeneous ruled surfaces. We also describe these cone structures in terms of solutions to new integrable systems admitting dispersionless, non-isospectral Lax pairs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10564 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cone structures and path geometries with constant torsion Kryński, Wojciech Differential Geometry We study three-dimensional path geometries with nontrivial torsion of maximal rank. We introduce the notion of constant torsion and show that such path geometries are in one-to-one correspondence with certain cone structures modeled on homogeneous ruled surfaces. We also describe these cone structures in terms of solutions to new integrable systems admitting dispersionless, non-isospectral Lax pairs. |
| title | Cone structures and path geometries with constant torsion |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2508.10564 |