Superfícies Weingarten generalizada tipo harmônico no espaço hiperbólico
Autor(a) principal: | |
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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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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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[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. 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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 |
600 600 600 600 |
dc.relation.department.fl_str_mv |
-4268777512335152015 |
dc.relation.cnpq.fl_str_mv |
6357880884991220629 |
dc.relation.sponsorship.fl_str_mv |
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[8] Blaschke, W.; Vorlesungen unber Differential geometrie, 3, Springer-Verlang, Berlin, 1929. [9] Bobenko, A.; Kitaev, A.; Surfaces with Harmonic Inverse Mean Curvature and Painlevé Equations [10] Bryant, R.L.; Surfaces of Mean Curvature One in Hyperbolic Space, Astérisque,154-155, 1987. [11] Collin, P.; Hauswirth, L.; Rosenberg, H.; The geometry of finite topology Bryant Surfaces, Ann. of Math, 153, 623-659, 2001. [12] Corro, A. V.; GeneralizedWeingarten Surfaces of Bryant type in hyperbolic 3-space, XIV School on Differential Geometry (Portuguese) Mat. Contemp. 30 (2006) 71-89. [13] Corro, A. V.; Riveros, C.M.C.; Surfaces with constant Chebyshev Angle Tokyo Journal of Mathematics. Vol 35. no 2 pp 359-366. December 2012. [14] Corro, A. V.; Riveros, C.M.C.; Surfaces with constant Chebyshev Angle II preprint. [15] Corro, A. V.; Pina, R., Souza, M.; Surfaces of Rotation with Constant Extrinsic Curvature in a Conformally Flat 3-Space, Results. Math. 60 (2011), 225-234. 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[30] Roitman, P.; de Lima, L.L.; Constante mean curvature one surfaces in hyperbolic 3- space using the Bianchi-Calò method, Annals of the Brazilian Academy of Sciences, 74, 19-24, 2002. [31] Rudin, W.; Real and complex analysis, McGraw-Hill international editions, 235, 1921. 3a edição. [32] Schief, W.K.; On Laplace-Darboux-type sequences of generalized Weingarten Surfaces, Journal of Mathematical physics, V.41, 9, 6566-6599, 2000. [33] Small, A.J.; Surfaces of constant mean curvature 1 in H3 and algebraic curves on a quadric, P. Am. Math. Soc.122, 1211-1220,1994. [34] Song, Y. P.; Wang, C. P.;Laguerre Minimal Surfaces in R3, Acta Math. Sinica vol 24, 1861-1870, 2008 [35] Tenenblat, K.; Introdução à Geometria Diferencial, Editora da Unb, Brasília, 1998. 1a reimpressão. [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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