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Special Weingarten surfaces foliated by circles

Rafael López
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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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Rafael López. 2006-07-28. Special Weingarten surfaces foliated by circles. https://arxiv.org/abs/math/0607749

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