Rotational Ricci surfaces
Differential Geometry
2024-02-20 v2
Abstract
We classify rotational surfaces in the three-dimensional Euclidean space whose Gaussian curvature satisfies \begin{equation*} K\Delta K - \|\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.
Keywords
Cite
@article{arxiv.2306.12307,
title = {Rotational Ricci surfaces},
author = {Iury Domingos and Roney Santos and Feliciano Vitório},
journal= {arXiv preprint arXiv:2306.12307},
year = {2024}
}
Comments
Term "free boundary" in Section 4 changed for "meeting the boundary orthogonally". Final version to appear in Ann. Mat. Pura Appl