On linear Weingarten surfaces
نویسنده
چکیده
In this paper we study surfaces in Euclidean 3-space that satisfy a Weingarten condition of linear type as κ1 = mκ2 + n, where m and n are real numbers and κ1 and κ2 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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