Superfícies Weingarten generalizada tipo harmônico no espaço hiperbólico

Detalhes bibliográficos
Autor(a) principal: Fernandes, Karoline Victor
Data de Publicação: 2013
Tipo de documento: Tese
Idioma: por
Título da fonte: Repositório Institucional da UFG
Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/3088
Resumo: 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.
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spelling Corro, Armando Mauro Vasquezhttp://lattes.cnpq.br/4498595305431615http://lattes.cnpq.br/1009292729883066Fernandes, Karoline Victor2014-09-18T15:39:54Z2013-09-20FERNANDES, Karoline Victor. Superfícies Weingarten generalizada tipo harmônico no espaço hiperbólico. 2013. 82 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2013.http://repositorio.bc.ufg.br/tede/handle/tede/3088ark:/38995/001300000dhr3In 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.Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2014-09-18T15:23:14Z No. of bitstreams: 2 Tese Karoline V Fernandes.pdf: 2432359 bytes, checksum: a5e472f248ce707b5697190ca4b6d33e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2014-09-18T15:39:54Z (GMT) No. of bitstreams: 2 Tese Karoline V Fernandes.pdf: 2432359 bytes, checksum: a5e472f248ce707b5697190ca4b6d33e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Made available in DSpace on 2014-09-18T15:39:54Z (GMT). No. of bitstreams: 2 Tese Karoline V Fernandes.pdf: 2432359 bytes, checksum: a5e472f248ce707b5697190ca4b6d33e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-09-20Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESapplication/pdfhttp://repositorio.bc.ufg.br/tede/retrieve/7918/Tese%20Karoline%20V%20Fernandes.pdf.jpgporUniversidade Federal de GoiásPrograma de Pós-graduação em Matemática (IME)UFGBrasilInstituto de Matemática e Estatística - IME (RG)[1] Ahlfors, L. V.; Complex Analysis, an introduction to the theory of analytic functions of one complex variable, McGraw-Hill Book Company, 4a edição. 1966. [2] Ávila, G.; Cálculo 3, funções de várias variáveis 3a edição, Rio de Janeiro, LTC - Livros Técnicos e Científicos Editora S.A. pg 196, 1983. [3] Barbosa, J.L.M.; Colares, A.G.; Minimal Surfaces in R3 Monografias de Matemática no 40, Impa. 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dc.title.por.fl_str_mv Superfícies Weingarten generalizada tipo harmônico no espaço hiperbólico
dc.title.alternative.eng.fl_str_mv Generalized Weingarten surfaces of harmonic type in hyperbolic space
title Superfícies Weingarten generalizada tipo harmônico no espaço hiperbólico
spellingShingle Superfícies Weingarten generalizada tipo harmônico no espaço hiperbólico
Fernandes, Karoline Victor
Congruência de esferas
Equação de Liouville
Superfície Weingarten generalizada
Congruence of spheres
Liouville equation
Generalized Weingarten surface
MATEMATICA::GEOMETRIA E TOPOLOGIA
title_short Superfícies Weingarten generalizada tipo harmônico no espaço hiperbólico
title_full Superfícies Weingarten generalizada tipo harmônico no espaço hiperbólico
title_fullStr Superfícies Weingarten generalizada tipo harmônico no espaço hiperbólico
title_full_unstemmed Superfícies Weingarten generalizada tipo harmônico no espaço hiperbólico
title_sort Superfícies Weingarten generalizada tipo harmônico no espaço hiperbólico
author Fernandes, Karoline Victor
author_facet Fernandes, Karoline Victor
author_role author
dc.contributor.advisor1.fl_str_mv Corro, Armando Mauro Vasquez
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/4498595305431615
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/1009292729883066
dc.contributor.author.fl_str_mv Fernandes, Karoline Victor
contributor_str_mv Corro, Armando Mauro Vasquez
dc.subject.por.fl_str_mv Congruência de esferas
Equação de Liouville
Superfície Weingarten generalizada
topic Congruência de esferas
Equação de Liouville
Superfície Weingarten generalizada
Congruence of spheres
Liouville equation
Generalized Weingarten surface
MATEMATICA::GEOMETRIA E TOPOLOGIA
dc.subject.eng.fl_str_mv Congruence of spheres
Liouville equation
Generalized Weingarten surface
dc.subject.cnpq.fl_str_mv MATEMATICA::GEOMETRIA E TOPOLOGIA
description 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.
publishDate 2013
dc.date.issued.fl_str_mv 2013-09-20
dc.date.accessioned.fl_str_mv 2014-09-18T15:39:54Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/doctoralThesis
format doctoralThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv FERNANDES, Karoline Victor. Superfícies Weingarten generalizada tipo harmônico no espaço hiperbólico. 2013. 82 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2013.
dc.identifier.uri.fl_str_mv http://repositorio.bc.ufg.br/tede/handle/tede/3088
dc.identifier.dark.fl_str_mv ark:/38995/001300000dhr3
identifier_str_mv FERNANDES, Karoline Victor. Superfícies Weingarten generalizada tipo harmônico no espaço hiperbólico. 2013. 82 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2013.
ark:/38995/001300000dhr3
url http://repositorio.bc.ufg.br/tede/handle/tede/3088
dc.language.iso.fl_str_mv por
language por
dc.relation.program.fl_str_mv 6600717948137941247
dc.relation.confidence.fl_str_mv 600
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600
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dc.relation.department.fl_str_mv -4268777512335152015
dc.relation.cnpq.fl_str_mv 6357880884991220629
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dc.relation.references.por.fl_str_mv [1] Ahlfors, L. V.; Complex Analysis, an introduction to the theory of analytic functions of one complex variable, McGraw-Hill Book Company, 4a edição. 1966. [2] Ávila, G.; Cálculo 3, funções de várias variáveis 3a edição, Rio de Janeiro, LTC - Livros Técnicos e Científicos Editora S.A. pg 196, 1983. [3] Barbosa, J.L.M.; Colares, A.G.; Minimal Surfaces in R3 Monografias de Matemática no 40, Impa. [4] Barbosa, J.L.; Sa Earp, R.; Prescribed mean curvature hypersurfaces in Hn+1(1) with convex planar boundary, I. , Geom. Dedicata 71, 61-74, 1998. [5] Barbosa, J.L.; Sa Earp, R.; Prescribed mean curvature hypersurfaces in Hn+1 with convex planar boundary, II ,Séminaire de théorie spectrale et géometrie de Grenoble, 16, 43-79, 1998. [6] Berger, M. S.; Constant scalar curvature metrics for complex manifolds In: Proceedings of Simposia in Pure Mathematics. Amer. Math. Soc. XXVII, part2, 153-170 (1975). 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Differential Geom., 60, 55- 101, 2002. [22] Leite, M. ; Brito, F.; Uniqueness and globality of the Liouville formula for entire solutions of ¶2 lnl ¶z¶z l 2a2 = 0, Arch. Math. 80, 501-506, 2003. [23] Li, T. Z.; Laguerre Geometry of Surfaces in R3, Acta Mathematica Sinica, Vol 21, n 06, pp 1525-1534, 2005. [24] Lima, E. L.; Curso de Análise volume 2, Projeto Euclides, Impa, Rio de Janeiro, 2008, 10a edição. [25] Liouville, J.; Sur l’équation aux differences partielles ¶2 lnl ¶z¶z l 2a2 = 0, J. Math. Pure Appl.36, 71-72,1853. [26] Miyagaki, H. O.; Equações elípticas modeladas em variedades riemannianas: uma introduçãoApresentado em Milênio Workshop em equações elípticas, 2004. [27] Musso, E.; Nicolodi, L.; A variational problem for surfaces in Laguerre geometry, Trans. Amer. Math. Soc., 348, 4321-4337, 1996. [28] Musso, E.; Nicolodi, L.; Laguerre geometry of surfaces with plane lines of curvature, Abh. Math. Sem. Univ. Hamburg, 69, 123-138, 1999. 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[36] Tenenblat, K,; Transformations of Manifolds and Applications to Differential Equations, International Conference on Differential Geometry, Impa, Rio de Janeiro, Julho 1996. [37] Toubiana, E.; Sa Earp, R.; Meromorphic data for mean curvature one surfaces in Hyperbolic three-space, Tohoku Math.J. 56, 1, 27-64, 2004. [38] Toubiana, E.; Sa Earp, R.; On the geometry of constant mean curvature one surfaces in hyperbolic space, To appear in Illinois Journal of Mathematics. [39] Toubiana, E.; Sa Earp, R.; Symmetry of properly embedded special Weingarten surfaces in H3 ,Trans. Am. Math. Soc. 351, 4693-4711, 1999. [40] Toubiana, E.; Sa Earp, R.; Existence and uniqueness of minimal graphs in hyperbolic space, To appear in Asian Journal of Mathematics. [41] Toubiana, E.; Sa Earp, R.; Some applications of maximum principle to hypersurfaces theory in euclidean and hyperbolic space,New Approaches in Nonlinear Analysis ( T. M. Rassias, Hadronic Press Inc, Florida, USA), 183-202, 1999. [42] Toubiana, E.; Sa Earp, R.; Introduction à la géométrie hyperbolique et aux surfaces de Riemann, Diderot Editeur, 1997. [43] Umehara, M., Yamada, K.; A parametrization of the Weierstrass formulae and pertubation of complete minimal surfaces in R3 into the hyperbolic 3-space, J. Reine Angew. Math., 432, 93-116, 1992. [44] Umehara, M., Yamada, K.; Complete surfaces of constant mean curvature-1 in the hyperbolic 3-space, Ann. of Math. 137, 611-638, 1993. [45] Umehara, M., Yamada, K.; Surfaces of constant mean curvature-c in H3(c2) with prescribed hyperbolic Gauss map , Math. Ann. 304, 203-224, 1996.
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