Closed $p$-Elastic Curves in Spheres of $\mathbb{L}^3$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912838893699072 |
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| author | Pampano, Alvaro Samarakkody, Miraj Tran, Hung |
| author_facet | Pampano, Alvaro Samarakkody, Miraj Tran, Hung |
| contents | For every $p\in\mathbb{R}$, we study $p$-elastic curves in the hyperbolic plane $\mathbb{H}^2$ and in the de Sitter $2$-space $\mathbb{H}_1^2$. We analyze the existence of closed $p$-elastic curves with nonconstant curvature showing that in the hyperbolic plane $\mathbb{H}^2$ these curves exist provided that $p>1$, while in the de Sitter $2$-space $\mathbb{H}_1^2$ the restriction $p<0$ must be satisfied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08593 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Closed $p$-Elastic Curves in Spheres of $\mathbb{L}^3$ Pampano, Alvaro Samarakkody, Miraj Tran, Hung Differential Geometry For every $p\in\mathbb{R}$, we study $p$-elastic curves in the hyperbolic plane $\mathbb{H}^2$ and in the de Sitter $2$-space $\mathbb{H}_1^2$. We analyze the existence of closed $p$-elastic curves with nonconstant curvature showing that in the hyperbolic plane $\mathbb{H}^2$ these curves exist provided that $p>1$, while in the de Sitter $2$-space $\mathbb{H}_1^2$ the restriction $p<0$ must be satisfied. |
| title | Closed $p$-Elastic Curves in Spheres of $\mathbb{L}^3$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2404.08593 |