Hipersuperfícies de tipo Ribaucour
| Ano de defesa: | 2022 |
|---|---|
| Autor(a) principal: |
Cárdenas Mendez, Milton Javier
 |
| Orientador(a): |
Vasquez Corro, Armando Mauro
|
| Banca de defesa: | , , , , |
| Tipo de documento: | Tese |
| Tipo de acesso: | Acesso aberto |
| Idioma: | por |
| Instituição de defesa: |
Universidade Federal de Goiás
|
| Programa de Pós-Graduação: |
Programa de Pós-graduação em Matemática (IME)
|
| Departamento: |
Instituto de Matemática e Estatística - IME (RG)
|
| País: |
Brasil
|
| Palavras-chave em Português: | |
| Palavras-chave em Inglês: | |
| Área do conhecimento CNPq: | |
| Link de acesso: | http://repositorio.bc.ufg.br/tede/handle/tede/12433 |
Resumo: | In this work we define the Ribaucour-type surfaces (in short, RT-surfaces),These surfaces satisfy a relationship similar to the Ribaucour surfaces that are related to the Élie Cartan problem. This class furnishes what seems to be the first examples of pairs of noncongruent surfaces in Euclidean space such that, under a diffeomorphism, lines of curvatures are preserved and principal curvatures are switched. We show that every compact and connected RT-surface is the sphere with center at the origin. We obtain present a Weierstrass type representation for RT-surfaces with prescribed Gauss map which depends on two holomorphic functions. We give explicit examples of RT-surfaces. Also, we use this representation to classify the RT-surfaces of rotation. We define the GRT-surfaces which are a generalization of the RT-surfaces, show a local parameterization of this class of surfaces and classify them in the in which case they are of rotation and generalize as RT-surfaces for the case of hypersurfaces in Rn+1, display a parameterizationção for the rotational cases and analyze the general of generatrix curves when hypersurfaces and rotation behavior are 3-dimensional. |
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Vasquez Corro, Armando Maurohttp://lattes.cnpq.br/4498595305431615Vasquez Corro, Armando MauroLeandro Neto, BeneditoCarrion Riveros, Carlos MaberSantos, João Paulo dosAdriano, Levi Rosahttp://lattes.cnpq.br/5426342188040232Cárdenas Mendez, Milton Javier2022-11-10T13:49:36Z2022-11-10T13:49:36Z2022-09-27MENDEZ, M. J. C. Hipersuperfícies de tipo Ribaucour. 2022. 72 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás,Goiânia, 2022.http://repositorio.bc.ufg.br/tede/handle/tede/12433In this work we define the Ribaucour-type surfaces (in short, RT-surfaces),These surfaces satisfy a relationship similar to the Ribaucour surfaces that are related to the Élie Cartan problem. This class furnishes what seems to be the first examples of pairs of noncongruent surfaces in Euclidean space such that, under a diffeomorphism, lines of curvatures are preserved and principal curvatures are switched. We show that every compact and connected RT-surface is the sphere with center at the origin. We obtain present a Weierstrass type representation for RT-surfaces with prescribed Gauss map which depends on two holomorphic functions. We give explicit examples of RT-surfaces. Also, we use this representation to classify the RT-surfaces of rotation. We define the GRT-surfaces which are a generalization of the RT-surfaces, show a local parameterization of this class of surfaces and classify them in the in which case they are of rotation and generalize as RT-surfaces for the case of hypersurfaces in Rn+1, display a parameterizationção for the rotational cases and analyze the general of generatrix curves when hypersurfaces and rotation behavior are 3-dimensional.Neste trabalho definimos as superfícies do tipo Ribaucour (abreviadamente, superfícies- TR). Essas superfícies satisfazem uma relação semelhante as superfícies de Ribaucour que estão relacionadas ao problema de Élie Cartan. Esta classe fornece o que parece ser o primeiro exemplo de pares de superfícies não congruentes no espaço euclidiano tal que, sob um difeomorfismo, as linhas de curvatura são preservadas e as curvaturas principais são trocadas. Mostramos que toda superfícies-TR compacta e conexa é a esfera com centro na origem. Obtemos uma representação do tipo Weierstrass para superfícies-TR com aplicação normal de Gauss prescrito que depende de duas funções holomorfas. Apresentamos exemplos explícitos de superfícies-TR. Além disso, usamos essa representação para classificar as superfícies-TR de rotação. Definimos as superfícies- TRG que é uma generalização das superfícies-TR, mostramos uma parametrização local desta classe de superfícies e classificamos no caso em que são de rotação e generalizamos as superfícies-TR para o caso de hipersuperfícies em Rn+1, exibimos uma parametrização para os casos rotacionais e analisamos o comportamento geral das curvas geratrizes quando as hipersuperfícies de rotação são 3-dimensionais.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESporUniversidade Federal de GoiásPrograma de Pós-graduação em Matemática (IME)UFGBrasilInstituto de Matemática e Estatística - IME (RG)Attribution-NonCommercial-NoDerivatives 4.0 Internationalinfo:eu-repo/semantics/openAccessSuperfícies de RibaucourSuperfície Weingarten generalizadaRepresentação de WeierstrassRibaucour surfacesGeneralized Weingarten surfacesWeierstrass type representationCIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIAHipersuperfícies de tipo RibaucourRibaucour-type surfacesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis70500500500500277941reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGORIGINALTese - Milton Javier Cárdenas Mendez - 2022.pdfTese - Milton Javier Cárdenas Mendez - 2022.pdfapplication/pdf2087993http://repositorio.bc.ufg.br/tede/bitstreams/ce8b3772-d2fd-4acb-be5d-89f8dd98e2e4/download61983e0f13954af76776a89538b822e9MD53LICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://repositorio.bc.ufg.br/tede/bitstreams/0b81b57b-6e38-437f-a0ea-5dca7e7dbbf3/download8a4605be74aa9ea9d79846c1fba20a33MD54CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805http://repositorio.bc.ufg.br/tede/bitstreams/4d308e87-326c-486b-8b32-b91b6ef2568e/download4460e5956bc1d1639be9ae6146a50347MD55tede/124332022-11-10 10:49:37.135http://creativecommons.org/licenses/by-nc-nd/4.0/Attribution-NonCommercial-NoDerivatives 4.0 Internationalopen.accessoai:repositorio.bc.ufg.br:tede/12433http://repositorio.bc.ufg.br/tedeRepositório InstitucionalPUBhttps://repositorio.bc.ufg.br/tedeserver/oai/requestgrt.bc@ufg.bropendoar:oai:repositorio.bc.ufg.br:tede/12342022-11-10T13:49:37Repositório Institucional da UFG - Universidade Federal de Goiás (UFG)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 |
| dc.title.pt_BR.fl_str_mv |
Hipersuperfícies de tipo Ribaucour |
| dc.title.alternative.eng.fl_str_mv |
Ribaucour-type surfaces |
| title |
Hipersuperfícies de tipo Ribaucour |
| spellingShingle |
Hipersuperfícies de tipo Ribaucour Cárdenas Mendez, Milton Javier Superfícies de Ribaucour Superfície Weingarten generalizada Representação de Weierstrass Ribaucour surfaces Generalized Weingarten surfaces Weierstrass type representation CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA |
| title_short |
Hipersuperfícies de tipo Ribaucour |
| title_full |
Hipersuperfícies de tipo Ribaucour |
| title_fullStr |
Hipersuperfícies de tipo Ribaucour |
| title_full_unstemmed |
Hipersuperfícies de tipo Ribaucour |
| title_sort |
Hipersuperfícies de tipo Ribaucour |
| author |
Cárdenas Mendez, Milton Javier |
| author_facet |
Cárdenas Mendez, Milton Javier |
| author_role |
author |
| dc.contributor.advisor1.fl_str_mv |
Vasquez Corro, Armando Mauro |
| dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/4498595305431615 |
| dc.contributor.referee1.fl_str_mv |
Vasquez Corro, Armando Mauro |
| dc.contributor.referee2.fl_str_mv |
Leandro Neto, Benedito |
| dc.contributor.referee3.fl_str_mv |
Carrion Riveros, Carlos Maber |
| dc.contributor.referee4.fl_str_mv |
Santos, João Paulo dos |
| dc.contributor.referee5.fl_str_mv |
Adriano, Levi Rosa |
| dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/5426342188040232 |
| dc.contributor.author.fl_str_mv |
Cárdenas Mendez, Milton Javier |
| contributor_str_mv |
Vasquez Corro, Armando Mauro Vasquez Corro, Armando Mauro Leandro Neto, Benedito Carrion Riveros, Carlos Maber Santos, João Paulo dos Adriano, Levi Rosa |
| dc.subject.por.fl_str_mv |
Superfícies de Ribaucour Superfície Weingarten generalizada Representação de Weierstrass |
| topic |
Superfícies de Ribaucour Superfície Weingarten generalizada Representação de Weierstrass Ribaucour surfaces Generalized Weingarten surfaces Weierstrass type representation CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA |
| dc.subject.eng.fl_str_mv |
Ribaucour surfaces Generalized Weingarten surfaces Weierstrass type representation |
| dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA |
| description |
In this work we define the Ribaucour-type surfaces (in short, RT-surfaces),These surfaces satisfy a relationship similar to the Ribaucour surfaces that are related to the Élie Cartan problem. This class furnishes what seems to be the first examples of pairs of noncongruent surfaces in Euclidean space such that, under a diffeomorphism, lines of curvatures are preserved and principal curvatures are switched. We show that every compact and connected RT-surface is the sphere with center at the origin. We obtain present a Weierstrass type representation for RT-surfaces with prescribed Gauss map which depends on two holomorphic functions. We give explicit examples of RT-surfaces. Also, we use this representation to classify the RT-surfaces of rotation. We define the GRT-surfaces which are a generalization of the RT-surfaces, show a local parameterization of this class of surfaces and classify them in the in which case they are of rotation and generalize as RT-surfaces for the case of hypersurfaces in Rn+1, display a parameterizationção for the rotational cases and analyze the general of generatrix curves when hypersurfaces and rotation behavior are 3-dimensional. |
| publishDate |
2022 |
| dc.date.accessioned.fl_str_mv |
2022-11-10T13:49:36Z |
| dc.date.available.fl_str_mv |
2022-11-10T13:49:36Z |
| dc.date.issued.fl_str_mv |
2022-09-27 |
| dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
| dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
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doctoralThesis |
| status_str |
publishedVersion |
| dc.identifier.citation.fl_str_mv |
MENDEZ, M. J. C. Hipersuperfícies de tipo Ribaucour. 2022. 72 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás,Goiânia, 2022. |
| dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/12433 |
| identifier_str_mv |
MENDEZ, M. J. C. Hipersuperfícies de tipo Ribaucour. 2022. 72 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás,Goiânia, 2022. |
| url |
http://repositorio.bc.ufg.br/tede/handle/tede/12433 |
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por |
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por |
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70 |
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500 500 500 500 |
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27 |
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794 |
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1 |
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Attribution-NonCommercial-NoDerivatives 4.0 International info:eu-repo/semantics/openAccess |
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Attribution-NonCommercial-NoDerivatives 4.0 International |
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openAccess |
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Universidade Federal de Goiás |
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Programa de Pós-graduação em Matemática (IME) |
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UFG |
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Brasil |
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Instituto de Matemática e Estatística - IME (RG) |
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Universidade Federal de Goiás |
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