Channel linear Weingarten surfaces in space forms
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2021
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909273917751296 |
|---|---|
| author | Hertrich-Jeromin, Udo Pember, Mason Polly, Denis |
| author_facet | Hertrich-Jeromin, Udo Pember, Mason Polly, Denis |
| contents | Channel linear Weingarten surfaces in space forms are investigated in a Lie sphere geometric setting, which allows for a uniform treatment of different ambient geometries. We show that any channel linear Weingarten surface in a space form is isothermic and, in particular, a surface of revolution in its ambient space form. We obtain explicit parametrisations for channel surfaces of constant Gauss curvature in space forms, and thereby for a large class of linear Weingarten surfaces up to parallel transformation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_00702 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Channel linear Weingarten surfaces in space forms Hertrich-Jeromin, Udo Pember, Mason Polly, Denis Differential Geometry 53A10 (primary), 53A40, 53C42, 37K35, 37K25 Channel linear Weingarten surfaces in space forms are investigated in a Lie sphere geometric setting, which allows for a uniform treatment of different ambient geometries. We show that any channel linear Weingarten surface in a space form is isothermic and, in particular, a surface of revolution in its ambient space form. We obtain explicit parametrisations for channel surfaces of constant Gauss curvature in space forms, and thereby for a large class of linear Weingarten surfaces up to parallel transformation. |
| title | Channel linear Weingarten surfaces in space forms |
| topic | Differential Geometry 53A10 (primary), 53A40, 53C42, 37K35, 37K25 |
| url | https://arxiv.org/abs/2105.00702 |