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Previous issue date: 2013-09-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we study surfaces M in hyperbolic space whose mean curvature H and
Gaussian curvature KI satisfy the relation 2(H 1)e2μ +KI(1e2μ) = 0; where μ is a
harmonic function with respect to the quadratic form s = KII + 2(H 1)II; and I,
II denote, respectively, the first and second quadratic form of M. These surfaces are
called Generalized Weingarten surfaces of harmonic type (HGW-surfaces). We obtain
a representation type Weierstrass for these surfaces that depend on three holomorphic
functions. As an application we obtain a representation type Weierstrass for Bryant
surfaces and classify all HGW-surfaces of rotation. / Neste trabalho estudamos superfícies M no espaço hiperbólico cuja curvatura média H e a
curvatura Gaussiana KI satisfazem a relação 2(H1)e2μ+KI(1e2μ) = 0; onde μ é uma
função harmônica com respeito a forma quadrática s = KII +2(H 1)II; onde I e II
são respectivamente a primeira e segunda forma quadrática de M. Estas superfícies serão
chamadas de Superfícies Weingarten generalizada tipo harmônico (Superfícies-WGH).
Obtemos uma representação tipo Weierstrass para estas superfícies que dependem de três
funções holomorfas. Como aplicação obtemos uma representação tipo Weierstrass para
superfícies de Bryant e classificamos as superfícies-WGH de rotação.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.bc.ufg.br:tede/3088 |
| Date | 20 September 2013 |
| Creators | Fernandes, Karoline Victor |
| Contributors | Corro, Armando Mauro Vasquez |
| Publisher | Universidade Federal de Goiás, Programa de Pós-graduação em Matemática (IME), UFG, Brasil, Instituto de Matemática e Estatística - IME (RG) |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | Portuguese |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/doctoralThesis |
| Format | application/pdf |
| Source | reponame:Biblioteca Digital de Teses e Dissertações da UFG, instname:Universidade Federal de Goiás, instacron:UFG |
| Rights | http://creativecommons.org/licenses/by-nc-nd/4.0/, info:eu-repo/semantics/openAccess |
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