Rotational Ricci surfaces

2023/06/21 by Domingos, Iury, Santos, Roney, Vitório, Feliciano
#53C42 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.12307

Abstract

We classify rotational surfaces in the three-dimensional Euclidean space whose Gaussian curvature K satisfies KΔK - ‖∇ K‖²-4K³ = 0. 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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