Superfícies de Weingarten Generalizadas do Tipo Rotacional no 3-Espaço Euclidiano
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2011-03-01
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Universidade Federal de Goiás
Resumo
In this work, we study the surfaces of rotation S which are Weingarten general, in which
the Gaussian curvature K and mean curvature H of this surface satisfies the following
relationship (w2 􀀀r2)K +2wH +1 = 0, where w and r are harmonic functions with
respect to the quadratic form s = II +wIII and II, III are the surface s second and third
quadratic form. Inspired by the work of Schief [15], we obtain a characterization of these
surfaces determined by functions satisfying a system of ordinary differential equations,
as application we prove that with an additional condition these surfaces are spheres.
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Citação
VELASCO, Lívio José. Generalized Weingarten Surfaces of Rotation in 3-
Euclidiano Space. 2011. 58 f. Dissertação (Mestrado em Ciências Exatas e da Terra) - Universidade Federal de Goiás, Goiânia, 2011.