On linear Weingarten surfaces

Rafael López

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arXiv · math/0607748

On linear Weingarten surfaces

Rafael López

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Abstract

In this paper we study surfaces in Euclidean 3-space that satisfy a Weingarten condition of linear type as $κ_1=m κ_2 +n$, where $m$ and $n$ are real numbers and $κ_1$ and $κ_2$ denote the principal curvatures at each point of the surface. We investigate the possible existence of such surfaces parametrized by a uniparametric family of circles. Besides the surfaces of revolution, we prove that not exist more except the case $(m,n)=(-1,0)$, that is, if the surface is one of the classical examples of minimal surfaces discovered by Riemann.

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BibTeX RIS

Rafael López. 2006-07-28. On linear Weingarten surfaces. https://arxiv.org/abs/math/0607748

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