Helicoidal minimal surfaces in the 3-sphere: An approach via spherical curves
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929260440059904 |
|---|---|
| author | Castro, Ildefonso Castro-Infantes, Ildefonso Castro-Infantes, Jesús |
| author_facet | Castro, Ildefonso Castro-Infantes, Ildefonso Castro-Infantes, Jesús |
| contents | We prove an existence and uniqueness theorem about spherical helicoidal (in particular, rotational) surfaces with prescribed mean or Gaussian curvature in terms of a continuous function depending on the distance to its axis. As an application in the case of vanishing mean curvature, it is shown that the well-known conjugation between the belicoid and the catenoid in Euclidean three-space extends naturally to the 3-sphere to their spherical versions and determine in a quite explicit way their associated surfaces in the sense of Lawson. As a key tool, we use the notion of spherical angular momentum of the spherical curves that play the role of profile curves of the minimal helicoidal surfaces in the 3-sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_08043 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Helicoidal minimal surfaces in the 3-sphere: An approach via spherical curves Castro, Ildefonso Castro-Infantes, Ildefonso Castro-Infantes, Jesús Differential Geometry Primary 53A04, Secondary 74H05 We prove an existence and uniqueness theorem about spherical helicoidal (in particular, rotational) surfaces with prescribed mean or Gaussian curvature in terms of a continuous function depending on the distance to its axis. As an application in the case of vanishing mean curvature, it is shown that the well-known conjugation between the belicoid and the catenoid in Euclidean three-space extends naturally to the 3-sphere to their spherical versions and determine in a quite explicit way their associated surfaces in the sense of Lawson. As a key tool, we use the notion of spherical angular momentum of the spherical curves that play the role of profile curves of the minimal helicoidal surfaces in the 3-sphere. |
| title | Helicoidal minimal surfaces in the 3-sphere: An approach via spherical curves |
| topic | Differential Geometry Primary 53A04, Secondary 74H05 |
| url | https://arxiv.org/abs/2303.08043 |