Rotational Ricci surfaces
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929246200397824 |
|---|---|
| author | Domingos, Iury Santos, Roney Vitório, Feliciano |
| author_facet | Domingos, Iury Santos, Roney Vitório, Feliciano |
| contents | We classify rotational surfaces in the three-dimensional Euclidean space whose Gaussian curvature $K$ satisfies
\begin{equation*}
KΔK - \|\nabla K\|^2-4K^3 = 0.
\end{equation*}
These surfaces are referred to as rotational Ricci surfaces. As an application, we show that there is a one-parameter family of such surfaces meeting the boundary of the unit Euclidean three-ball orthogonally. In addition, we show that this family interpolates a vertical geodesic and the critical catenoid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_12307 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rotational Ricci surfaces Domingos, Iury Santos, Roney Vitório, Feliciano Differential Geometry 53C42 We classify rotational surfaces in the three-dimensional Euclidean space whose Gaussian curvature $K$ satisfies \begin{equation*} KΔK - \|\nabla K\|^2-4K^3 = 0. \end{equation*} These surfaces are referred to as rotational Ricci surfaces. As an application, we show that there is a one-parameter family of such surfaces meeting the boundary of the unit Euclidean three-ball orthogonally. In addition, we show that this family interpolates a vertical geodesic and the critical catenoid. |
| title | Rotational Ricci surfaces |
| topic | Differential Geometry 53C42 |
| url | https://arxiv.org/abs/2306.12307 |