$h$-Principles for curves and knots of constant torsion
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916986050576384 |
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| author | Ghomi, Mohammad Raffaelli, Matteo |
| author_facet | Ghomi, Mohammad Raffaelli, Matteo |
| contents | We prove that curves of constant torsion satisfy the $C^1$-dense h-principle in the space of immersed curves in Euclidean space. In particular, there exists a knot of constant torsion in each isotopy class. Our methods, which involve convex integration and degree theory, quickly establish these results for curves of constant curvature as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06027 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $h$-Principles for curves and knots of constant torsion Ghomi, Mohammad Raffaelli, Matteo Differential Geometry Primary 53A04, 57K10, Secondary 58C35, 53C21 We prove that curves of constant torsion satisfy the $C^1$-dense h-principle in the space of immersed curves in Euclidean space. In particular, there exists a knot of constant torsion in each isotopy class. Our methods, which involve convex integration and degree theory, quickly establish these results for curves of constant curvature as well. |
| title | $h$-Principles for curves and knots of constant torsion |
| topic | Differential Geometry Primary 53A04, 57K10, Secondary 58C35, 53C21 |
| url | https://arxiv.org/abs/2410.06027 |