Superfícies de Weingarten Generalizadas do Tipo Rotacional no 3-Espaço Euclidiano

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Detalles Bibliográficos
Autor Principal:	VELASCO, Lívio José
Data de Publicación:	2011
Formato:	Master thesis
Idioma:	por
Fonte:	Repositório Institucional da UFG
Download full:	http://repositorio.bc.ufg.br/tede/handle/tde/1933
Summary:	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.

Descripción
Summary:	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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