Special Weingarten surfaces foliated by circles

2006/07/28 by Rafael López, López, Rafael
Mathematics · #53A05 #53C40 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.math/0607749

openalex publication_date 2006/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study surfaces in Euclidean 3-space foliated by pieces of circles and that satisfy a Weingarten condition of type a H+b K=c, where a,b and c are constant and H and K denote the mean curvature and the Gauss curvature respectively. We prove that a such surface must be a surface of revolution, a Riemann minimal surface or a generalized cone.

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