Classes de hipersuperfícies Weingarten generalizada no espaço euclidiano
Autor(a) principal: | |
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Data de Publicação: | 2014 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFG |
Texto Completo: | http://repositorio.bc.ufg.br/tede/handle/tede/4091 |
Resumo: | We present hypersurfaces with prescribed normal Gauss map. These surfaces are obtained as the envelope of a sphere congruence where the other envelope is contained in a plane. We introduce classes of surfaces that generalize linear Weingarten surfaces, where the coefficients are functions that depend on the support function and the distance function from a fixed point (in short, DSGW-surfaces). The linear Weingarten surfaces, the Appell’s surfaces and the Tzitzeica’s surfaces are all DSGW-surfaces. From them we obtain new classes of DSGW-surfaces applying inversions and dilatations. For a special class of DSGW-surfaces, which is invariant under dilatations and inversions, we obtain a Weierstrass type representation (in short, EDSGW-surfaces). As application we classify the EDSGW-surfaces of rotation and present a 4-parameter family of complete cyclic EDSGW-surfaces with an isolated singularity and foliated by non-parallel planes. We generalized the EDSGW-surfaces for the case of hypersurfaces in Rn+1, n ≥ 2. We present a representation for these hypersurfaces in the case where the stereographic projection of the normal Gauss map N is given by the identity application. As an application, we will characterize the rotational examples. |
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Corro, Armando M.V.http://lattes.cnpq.br/4498595305431615Corro, Armando M.V.Piccione, PaoloDorea, Chang C.Y.Ferreira, W.Adriano, Levihttp://lattes.cnpq.br/0440704592361801Dias, D. G.2015-02-05T11:02:53Z2014-09-29DIAS , D. G. Classes de hipersuperfícies Weingarten generalizada no espaço euclidiano. 2014. 68 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2014.http://repositorio.bc.ufg.br/tede/handle/tede/4091We present hypersurfaces with prescribed normal Gauss map. These surfaces are obtained as the envelope of a sphere congruence where the other envelope is contained in a plane. We introduce classes of surfaces that generalize linear Weingarten surfaces, where the coefficients are functions that depend on the support function and the distance function from a fixed point (in short, DSGW-surfaces). The linear Weingarten surfaces, the Appell’s surfaces and the Tzitzeica’s surfaces are all DSGW-surfaces. From them we obtain new classes of DSGW-surfaces applying inversions and dilatations. For a special class of DSGW-surfaces, which is invariant under dilatations and inversions, we obtain a Weierstrass type representation (in short, EDSGW-surfaces). As application we classify the EDSGW-surfaces of rotation and present a 4-parameter family of complete cyclic EDSGW-surfaces with an isolated singularity and foliated by non-parallel planes. We generalized the EDSGW-surfaces for the case of hypersurfaces in Rn+1, n ≥ 2. We present a representation for these hypersurfaces in the case where the stereographic projection of the normal Gauss map N is given by the identity application. As an application, we will characterize the rotational examples.Apresentamos parametrizações de hipersuperfícies com aplicação normal de Gauss prescrita. Estas parametrizações são obtidas como o envelope de uma congruência de esferas onde o outro envelope esta contido em um hiperplano. Introduzimos classes de superfícies que generalizam as superfícies de Weingarten linear, onde os coeficientes são funções que dependem da função suporte e da função distância a um ponto fixo (superfícies WGSD). Classes conhecidas destas superfícies são as superfícies de Weingarten linear, as superfícies de Appell e as superfícies de Tzitzéica. A partir delas obtemos novas classes de superfícies WGSD aplicando inversões e dilatações. Para uma classe especial de superfícies WGSD, que é invariante por dilatações e inversoes (superfícies WGSDE), obtemos uma representação tipo Weierstrass, dependendo de duas funções holomorfas. Como aplicação classificamos as superfícies WGSDE de rotação e apresentamos uma família a 4-parâmetros de superfícies WGSDE cíclicas completas com uma singularidade isolada e com planos de folheação não paralelos. Terminamos generalizando as superfícies WGSDE para o hipersuperfícies em Rn+1, n ≥ 2. Apresentaremos uma representação para estas hipersuperfícies no caso em que a projeção estereográfica da normal de Gauss N é dada pela aplicação identidade. Como aplicação, caracterizaremos os exemplos rotacionais.Submitted by Luanna Matias (lua_matias@yahoo.com.br) on 2015-02-05T10:44:34Z No. of bitstreams: 2 Tese - Diogo Gonçalves Dias - 2014.pdf.pdf: 490676 bytes, checksum: 3c0940e1fbec55f277f969c4751c5ea6 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-02-05T11:02:53Z (GMT) No. of bitstreams: 2 Tese - Diogo Gonçalves Dias - 2014.pdf.pdf: 490676 bytes, checksum: 3c0940e1fbec55f277f969c4751c5ea6 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Made available in DSpace on 2015-02-05T11:02:53Z (GMT). No. of bitstreams: 2 Tese - Diogo Gonçalves Dias - 2014.pdf.pdf: 490676 bytes, checksum: 3c0940e1fbec55f277f969c4751c5ea6 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-09-29Fundação de Amparo à Pesquisa do Estado de Goiás - FAPEGapplication/pdfhttp://repositorio.bc.ufg.br/tede/retrieve/16491/Tese%20-%20Diogo%20Gon%c3%a7alves%20Dias%20-%202014.pdf.pdf.jpgporUniversidade Federal de GoiásPrograma de Pós-graduação em Matemática (IME)UFGBrasilInstituto de Matemática e Estatística - IME (RG)http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessSuperfícies Weingarten generalizadaRepresentação tipo WeierstrassAplicação normal de Gauss prescritaGeneralized Weingarten surfacesWeierstrass type representationPrescribed normal Gauss mapALGEBRA::GEOMETRIA ALGEBRICAClasses de hipersuperfícies Weingarten generalizada no espaço euclidianoClasses of generalized Weingarten hypersurfaces in the euclidean spaceinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis6600717948137941247600600600600-4268777512335152015-1843471329842045595-961409807440757778reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; 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dc.title.eng.fl_str_mv |
Classes de hipersuperfícies Weingarten generalizada no espaço euclidiano |
dc.title.alternative.eng.fl_str_mv |
Classes of generalized Weingarten hypersurfaces in the euclidean space |
title |
Classes de hipersuperfícies Weingarten generalizada no espaço euclidiano |
spellingShingle |
Classes de hipersuperfícies Weingarten generalizada no espaço euclidiano Dias, D. G. Superfícies Weingarten generalizada Representação tipo Weierstrass Aplicação normal de Gauss prescrita Generalized Weingarten surfaces Weierstrass type representation Prescribed normal Gauss map ALGEBRA::GEOMETRIA ALGEBRICA |
title_short |
Classes de hipersuperfícies Weingarten generalizada no espaço euclidiano |
title_full |
Classes de hipersuperfícies Weingarten generalizada no espaço euclidiano |
title_fullStr |
Classes de hipersuperfícies Weingarten generalizada no espaço euclidiano |
title_full_unstemmed |
Classes de hipersuperfícies Weingarten generalizada no espaço euclidiano |
title_sort |
Classes de hipersuperfícies Weingarten generalizada no espaço euclidiano |
author |
Dias, D. G. |
author_facet |
Dias, D. G. |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Corro, Armando M.V. |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/4498595305431615 |
dc.contributor.referee1.fl_str_mv |
Corro, Armando M.V. |
dc.contributor.referee2.fl_str_mv |
Piccione, Paolo |
dc.contributor.referee3.fl_str_mv |
Dorea, Chang C.Y. |
dc.contributor.referee4.fl_str_mv |
Ferreira, W. |
dc.contributor.referee5.fl_str_mv |
Adriano, Levi |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/0440704592361801 |
dc.contributor.author.fl_str_mv |
Dias, D. G. |
contributor_str_mv |
Corro, Armando M.V. Corro, Armando M.V. Piccione, Paolo Dorea, Chang C.Y. Ferreira, W. Adriano, Levi |
dc.subject.por.fl_str_mv |
Superfícies Weingarten generalizada Representação tipo Weierstrass Aplicação normal de Gauss prescrita |
topic |
Superfícies Weingarten generalizada Representação tipo Weierstrass Aplicação normal de Gauss prescrita Generalized Weingarten surfaces Weierstrass type representation Prescribed normal Gauss map ALGEBRA::GEOMETRIA ALGEBRICA |
dc.subject.eng.fl_str_mv |
Generalized Weingarten surfaces Weierstrass type representation Prescribed normal Gauss map |
dc.subject.cnpq.fl_str_mv |
ALGEBRA::GEOMETRIA ALGEBRICA |
description |
We present hypersurfaces with prescribed normal Gauss map. These surfaces are obtained as the envelope of a sphere congruence where the other envelope is contained in a plane. We introduce classes of surfaces that generalize linear Weingarten surfaces, where the coefficients are functions that depend on the support function and the distance function from a fixed point (in short, DSGW-surfaces). The linear Weingarten surfaces, the Appell’s surfaces and the Tzitzeica’s surfaces are all DSGW-surfaces. From them we obtain new classes of DSGW-surfaces applying inversions and dilatations. For a special class of DSGW-surfaces, which is invariant under dilatations and inversions, we obtain a Weierstrass type representation (in short, EDSGW-surfaces). As application we classify the EDSGW-surfaces of rotation and present a 4-parameter family of complete cyclic EDSGW-surfaces with an isolated singularity and foliated by non-parallel planes. We generalized the EDSGW-surfaces for the case of hypersurfaces in Rn+1, n ≥ 2. We present a representation for these hypersurfaces in the case where the stereographic projection of the normal Gauss map N is given by the identity application. As an application, we will characterize the rotational examples. |
publishDate |
2014 |
dc.date.issued.fl_str_mv |
2014-09-29 |
dc.date.accessioned.fl_str_mv |
2015-02-05T11:02:53Z |
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 |
DIAS , D. G. Classes de hipersuperfícies Weingarten generalizada no espaço euclidiano. 2014. 68 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2014. |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/4091 |
identifier_str_mv |
DIAS , D. G. Classes de hipersuperfícies Weingarten generalizada no espaço euclidiano. 2014. 68 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2014. |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/4091 |
dc.language.iso.fl_str_mv |
por |
language |
por |
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6600717948137941247 |
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600 600 600 600 |
dc.relation.department.fl_str_mv |
-4268777512335152015 |
dc.relation.cnpq.fl_str_mv |
-1843471329842045595 |
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dc.rights.driver.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
http://creativecommons.org/licenses/by-nc-nd/4.0/ |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Universidade Federal de Goiás |
dc.publisher.program.fl_str_mv |
Programa de Pós-graduação em Matemática (IME) |
dc.publisher.initials.fl_str_mv |
UFG |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
Instituto de Matemática e Estatística - IME (RG) |
publisher.none.fl_str_mv |
Universidade Federal de Goiás |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFG instname:Universidade Federal de Goiás (UFG) instacron:UFG |
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Universidade Federal de Goiás (UFG) |
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