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arXiv · 2306.12307

Rotational Ricci surfaces

Iury Domingos·Roney Santos·Feliciano Vitório
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Abstract

We classify rotational surfaces in the three-dimensional Euclidean space whose Gaussian curvature $K$ 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.

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Iury Domingos, Roney Santos, Feliciano Vitório. 2023-06-21. Rotational Ricci surfaces. https://arxiv.org/abs/2306.12307

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