Polyharmonic helices
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909177353338880 |
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| author | Montaldo, Stefano Ratto, Andrea |
| author_facet | Montaldo, Stefano Ratto, Andrea |
| contents | The main aim of this paper is to investigate the existence of Frenet helices which are polyharmonic of order $r$, shortly, $r$-harmonic. We shall obtain existence, non-existence and classification results. More specifically, we obtain a complete classification of proper $r$-harmonic helices into the $3$-dimensional solvable Lie group Sol$_3$. Next, we investigate the existence of proper $r$-harmonic helices into Bianchi-Cartan-Vranceanu spaces and, in this context, we find new examples. Finally, we shall establish some non-existence results both for Frenet curves and Frenet helices of order $n \geq 4$ when the ambient space is the Euclidean sphere $\s^m$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13726 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polyharmonic helices Montaldo, Stefano Ratto, Andrea Differential Geometry The main aim of this paper is to investigate the existence of Frenet helices which are polyharmonic of order $r$, shortly, $r$-harmonic. We shall obtain existence, non-existence and classification results. More specifically, we obtain a complete classification of proper $r$-harmonic helices into the $3$-dimensional solvable Lie group Sol$_3$. Next, we investigate the existence of proper $r$-harmonic helices into Bianchi-Cartan-Vranceanu spaces and, in this context, we find new examples. Finally, we shall establish some non-existence results both for Frenet curves and Frenet helices of order $n \geq 4$ when the ambient space is the Euclidean sphere $\s^m$. |
| title | Polyharmonic helices |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2404.13726 |