Deformations of curves with constant curvature
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910912232816640 |
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| author | Ghomi, Mohammad Raffaelli, Matteo |
| author_facet | Ghomi, Mohammad Raffaelli, Matteo |
| contents | We prove that curves of constant curvature satisfy the parametric $C^1$-dense relative $h$-principle in the space of immersed curves with nonvanishing curvature in Euclidean space $R^{n\geq 3}$. It follows that two knots of constant curvature in $R^3$ are isotopic, resp. homotopic, through curves of constant curvature if and only if they are isotopic, resp. homotopic, and their self-linking numbers, resp. self-linking numbers mod $2$, are equal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01729 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deformations of curves with constant curvature Ghomi, Mohammad Raffaelli, Matteo Differential Geometry Geometric Topology Primary 53A04, 57K10, Secondary 58C35, 53C21 We prove that curves of constant curvature satisfy the parametric $C^1$-dense relative $h$-principle in the space of immersed curves with nonvanishing curvature in Euclidean space $R^{n\geq 3}$. It follows that two knots of constant curvature in $R^3$ are isotopic, resp. homotopic, through curves of constant curvature if and only if they are isotopic, resp. homotopic, and their self-linking numbers, resp. self-linking numbers mod $2$, are equal. |
| title | Deformations of curves with constant curvature |
| topic | Differential Geometry Geometric Topology Primary 53A04, 57K10, Secondary 58C35, 53C21 |
| url | https://arxiv.org/abs/2407.01729 |