Superfícies de Weingarten Lineares Hiperbólicas em R3

• Autor(a) principal: GUEDES, Luciene Viana
• Data de Publicação: 2009
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• dARK ID: ark:/38995/001300000b7bv
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tde/1963
• topic: Superfícies de Weingarten Lineares Hiperbólicas em R3; Geometria diferencial; Hyperbolic linear Weingarten surfaces in R3; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA

The present work has been based by the [1] from Juan A. Aledo S´anches and Jos´e M. Espinar and [2] from Rafael L´opez articles. In those articles they studied hiperbolic linear Weingarten surfaces in R3 space, this is, surface whose mean curvature H and Gaussian curvature K satisfy a relation of the form aH+bK =c, where a, b, c 2 R. A such surface is said to be hiperbolic when the discriminant D := a2+4bc < 0.We obtain a representation for rotational hyperbolic linear Weingarten surfaces in terms of its Gauss map and we also present, in the case a 6= 0, a classification of linearWeingarten surfaces of hyperbolic rotation. As a consequence we obtain, in the case a 6=0, a family of complete hyperbolic linear Weingarten surfaces in R3. This contrasts with Hilbert s theorem that there do not exist complete surfaces with constant negative Gaussian curvature immersed in R3.