Superfícies de Weingarten Lineares Hiperbólicas em R3
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Data
2009-08-25
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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.
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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.