Superfícies de Weingarten Lineares Hiperbólicas em R3
Data
2009-08-25
Autores
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Editor
Universidade Federal de Goiás
Resumo
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.
Descrição
Citação
GUEDES, Luciene Viana. Hyperbolic linear Weingarten surfaces in R3. 2009. 71 f. Dissertação (Mestrado em Ciências Exatas e da Terra) - Universidade Federal de Goiás, Goiânia, 2009.