A curvatura Gaussiana via ângulo de contato de superfícies imersas em S3
Autor(a) principal: | |
---|---|
Data de Publicação: | 2015 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFG |
Texto Completo: | http://repositorio.bc.ufg.br/tede/handle/tede/4550 |
Resumo: | In this work we refer to the study of a geometric invariant surfaces immersed in Euclidean 3-dimensional sphere S3. Such invariant, known as angle contact, is the complementary angle between the distribution of contact d and the tangent space of the surface. Montes and Verderesi [22] characterized the minimal surfaces in S3 with constant contact angle and Almeida, Brazil and Montes [4] studied some properties of immersed constant mean curvature into a round sphere S3 with constant contact angle. The our aim of this work is to deduce a general formula involving the Gaussian curvature, the mean curvature and the contact angle of surfaces immersed in Euclidean sphere 3-dimensional, which shows that the surface is flat if the contact angle is constant. Moreover, we deduce that the Clifford tori are the unique compact surfaces with constant mean curvature having such propriety. Keywords |
id |
UFG-2_aa944bd5f0e873d980aba0ebc85bb4ca |
---|---|
oai_identifier_str |
oai:repositorio.bc.ufg.br:tede/4550 |
network_acronym_str |
UFG-2 |
network_name_str |
Repositório Institucional da UFG |
repository_id_str |
|
spelling |
Corro, Armando Mauro Vasquezhttp://lattes.cnpq.br/4498595305431615Corro, Armando Mauro VasquezSantos, João Paulo dosPieterzack, Maurício Donizettihttp://lattes.cnpq.br/6914909788902260Argote, Fernando Arnulfo Zuñiga2015-05-19T14:50:54Z2015-02-27ARGOTE, F. A. Z. A curvatura Gaussiana via ângulo de contato de superfícies imersas em S3. 2015. 78 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2015.http://repositorio.bc.ufg.br/tede/handle/tede/4550In this work we refer to the study of a geometric invariant surfaces immersed in Euclidean 3-dimensional sphere S3. Such invariant, known as angle contact, is the complementary angle between the distribution of contact d and the tangent space of the surface. Montes and Verderesi [22] characterized the minimal surfaces in S3 with constant contact angle and Almeida, Brazil and Montes [4] studied some properties of immersed constant mean curvature into a round sphere S3 with constant contact angle. The our aim of this work is to deduce a general formula involving the Gaussian curvature, the mean curvature and the contact angle of surfaces immersed in Euclidean sphere 3-dimensional, which shows that the surface is flat if the contact angle is constant. Moreover, we deduce that the Clifford tori are the unique compact surfaces with constant mean curvature having such propriety. KeywordsNeste trabalho nos referimos ao estudo de um invariante geométrico de superfícies imersas na esfera Euclidiana 3-dimensional S3. Tal invariante, conhecido como ângulo de contato, é o complementar do ângulo entre a distribuição de contato d e o espaço tangente da superfície. Montes e Verderesi [22] caracterizaram as superfícies mínimas em S3 com ângulo de contato constante e Almeida, Brasil e Montes [4] estudaram algumas propriedades de superfícies imersas com curvatura média e ângulo de contato constantes em S3. Nosso objetivo será apresentar uma relação entre a curvatura Gaussiana, a curvatura média e o ângulo de contato de superfícies imersas na esfera Euclidiana 3-dimensional, a qual permite concluir que a superfície é plana se o ângulo de contato for constante. Além disso, concluiremos que o toro de Clifford é a única superfície compacta com curvatura média constante tendo tal propriedade.Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-05-19T14:40:22Z No. of bitstreams: 2 Dissertação - Fernando Arnulfo Zuniga Argote - 2015.pdf: 631746 bytes, checksum: 0d49f26d4f922ddd70836a2024ad5850 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-05-19T14:50:54Z (GMT) No. of bitstreams: 2 Dissertação - Fernando Arnulfo Zuniga Argote - 2015.pdf: 631746 bytes, checksum: 0d49f26d4f922ddd70836a2024ad5850 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Made available in DSpace on 2015-05-19T14:50:54Z (GMT). No. of bitstreams: 2 Dissertação - Fernando Arnulfo Zuniga Argote - 2015.pdf: 631746 bytes, checksum: 0d49f26d4f922ddd70836a2024ad5850 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-02-27Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPqapplication/pdfhttp://repositorio.bc.ufg.br/tede/retrieve/19988/Disserta%c3%a7%c3%a3o%20-%20Fernando%20Arnulfo%20Zuniga%20Argote%20-%202015.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 mínimasToro de CliffordCurvatura média constanteEsfera Euclidiana S3Ângulo de contatoMinimal surfacesClifford torusConstant mean curvatureEuclidian sphere S3Contact angleCIENCIAS EXATAS E DA TERRA::MATEMATICAA curvatura Gaussiana via ângulo de contato de superfícies imersas em S3The Gaussian curvature via the contact angle of immersed surfaces into the S3info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis6600717948137941247600600600600-4268777512335152015-7090823417984401694-2555911436985713659reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; charset=utf-82165http://repositorio.bc.ufg.br/tede/bitstreams/6d31798d-ca09-448c-80c6-0654b931e8a4/downloadbd3efa91386c1718a7f26a329fdcb468MD51CC-LICENSElicense_urllicense_urltext/plain; charset=utf-849http://repositorio.bc.ufg.br/tede/bitstreams/dd27c950-30c0-4f5c-832d-0b91f79f74d5/download4afdbb8c545fd630ea7db775da747b2fMD52license_textlicense_texttext/html; charset=utf-822762http://repositorio.bc.ufg.br/tede/bitstreams/f4b500dd-80f3-4abe-a1e5-6d4baadddacf/downloadfda13080e892f3f68def2b8b70227968MD53license_rdflicense_rdfapplication/rdf+xml; charset=utf-823148http://repositorio.bc.ufg.br/tede/bitstreams/96191a44-0182-4288-b8e3-98172b348599/download9da0b6dfac957114c6a7714714b86306MD54ORIGINALDissertação - Fernando Arnulfo Zuniga Argote - 2015.pdfDissertação - Fernando Arnulfo Zuniga Argote - 2015.pdfapplication/pdf631746http://repositorio.bc.ufg.br/tede/bitstreams/30e050ba-e711-4f66-aaaf-fbad21c91f71/download0d49f26d4f922ddd70836a2024ad5850MD55TEXTDissertação - Fernando Arnulfo Zuniga Argote - 2015.pdf.txtDissertação - Fernando Arnulfo Zuniga Argote - 2015.pdf.txtExtracted Texttext/plain123101http://repositorio.bc.ufg.br/tede/bitstreams/a2422f86-90b6-46ff-bf1f-01ea265cd10b/download22819b5eaff993a06ed4e8f1d1e19d03MD56THUMBNAILDissertação - Fernando Arnulfo Zuniga Argote - 2015.pdf.jpgDissertação - Fernando Arnulfo Zuniga Argote - 2015.pdf.jpgGenerated Thumbnailimage/jpeg3374http://repositorio.bc.ufg.br/tede/bitstreams/356010db-c0a3-4623-a2ea-7ac34b48c88a/download1c994ef5f3d66271e71b312205144228MD57tede/45502015-05-20 03:02:03.47http://creativecommons.org/licenses/by-nc-nd/4.0/Acesso Abertoopen.accessoai:repositorio.bc.ufg.br:tede/4550http://repositorio.bc.ufg.br/tedeRepositório InstitucionalPUBhttp://repositorio.bc.ufg.br/oai/requesttasesdissertacoes.bc@ufg.bropendoar:2015-05-20T06:02:03Repositório Institucional da UFG - Universidade Federal de Goiás (UFG)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 |
dc.title.por.fl_str_mv |
A curvatura Gaussiana via ângulo de contato de superfícies imersas em S3 |
dc.title.alternative.eng.fl_str_mv |
The Gaussian curvature via the contact angle of immersed surfaces into the S3 |
title |
A curvatura Gaussiana via ângulo de contato de superfícies imersas em S3 |
spellingShingle |
A curvatura Gaussiana via ângulo de contato de superfícies imersas em S3 Argote, Fernando Arnulfo Zuñiga Superfícies mínimas Toro de Clifford Curvatura média constante Esfera Euclidiana S3 Ângulo de contato Minimal surfaces Clifford torus Constant mean curvature Euclidian sphere S3 Contact angle CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
A curvatura Gaussiana via ângulo de contato de superfícies imersas em S3 |
title_full |
A curvatura Gaussiana via ângulo de contato de superfícies imersas em S3 |
title_fullStr |
A curvatura Gaussiana via ângulo de contato de superfícies imersas em S3 |
title_full_unstemmed |
A curvatura Gaussiana via ângulo de contato de superfícies imersas em S3 |
title_sort |
A curvatura Gaussiana via ângulo de contato de superfícies imersas em S3 |
author |
Argote, Fernando Arnulfo Zuñiga |
author_facet |
Argote, Fernando Arnulfo Zuñiga |
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.referee1.fl_str_mv |
Corro, Armando Mauro Vasquez |
dc.contributor.referee2.fl_str_mv |
Santos, João Paulo dos |
dc.contributor.referee3.fl_str_mv |
Pieterzack, Maurício Donizetti |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/6914909788902260 |
dc.contributor.author.fl_str_mv |
Argote, Fernando Arnulfo Zuñiga |
contributor_str_mv |
Corro, Armando Mauro Vasquez Corro, Armando Mauro Vasquez Santos, João Paulo dos Pieterzack, Maurício Donizetti |
dc.subject.por.fl_str_mv |
Superfícies mínimas Toro de Clifford Curvatura média constante Esfera Euclidiana S3 Ângulo de contato |
topic |
Superfícies mínimas Toro de Clifford Curvatura média constante Esfera Euclidiana S3 Ângulo de contato Minimal surfaces Clifford torus Constant mean curvature Euclidian sphere S3 Contact angle CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Minimal surfaces Clifford torus Constant mean curvature Euclidian sphere S3 Contact angle |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
In this work we refer to the study of a geometric invariant surfaces immersed in Euclidean 3-dimensional sphere S3. Such invariant, known as angle contact, is the complementary angle between the distribution of contact d and the tangent space of the surface. Montes and Verderesi [22] characterized the minimal surfaces in S3 with constant contact angle and Almeida, Brazil and Montes [4] studied some properties of immersed constant mean curvature into a round sphere S3 with constant contact angle. The our aim of this work is to deduce a general formula involving the Gaussian curvature, the mean curvature and the contact angle of surfaces immersed in Euclidean sphere 3-dimensional, which shows that the surface is flat if the contact angle is constant. Moreover, we deduce that the Clifford tori are the unique compact surfaces with constant mean curvature having such propriety. Keywords |
publishDate |
2015 |
dc.date.accessioned.fl_str_mv |
2015-05-19T14:50:54Z |
dc.date.issued.fl_str_mv |
2015-02-27 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
ARGOTE, F. A. Z. A curvatura Gaussiana via ângulo de contato de superfícies imersas em S3. 2015. 78 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2015. |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/4550 |
identifier_str_mv |
ARGOTE, F. A. Z. A curvatura Gaussiana via ângulo de contato de superfícies imersas em S3. 2015. 78 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2015. |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/4550 |
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 |
-7090823417984401694 |
dc.relation.sponsorship.fl_str_mv |
-2555911436985713659 |
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 |
instname_str |
Universidade Federal de Goiás (UFG) |
instacron_str |
UFG |
institution |
UFG |
reponame_str |
Repositório Institucional da UFG |
collection |
Repositório Institucional da UFG |
bitstream.url.fl_str_mv |
http://repositorio.bc.ufg.br/tede/bitstreams/6d31798d-ca09-448c-80c6-0654b931e8a4/download http://repositorio.bc.ufg.br/tede/bitstreams/dd27c950-30c0-4f5c-832d-0b91f79f74d5/download http://repositorio.bc.ufg.br/tede/bitstreams/f4b500dd-80f3-4abe-a1e5-6d4baadddacf/download http://repositorio.bc.ufg.br/tede/bitstreams/96191a44-0182-4288-b8e3-98172b348599/download http://repositorio.bc.ufg.br/tede/bitstreams/30e050ba-e711-4f66-aaaf-fbad21c91f71/download http://repositorio.bc.ufg.br/tede/bitstreams/a2422f86-90b6-46ff-bf1f-01ea265cd10b/download http://repositorio.bc.ufg.br/tede/bitstreams/356010db-c0a3-4623-a2ea-7ac34b48c88a/download |
bitstream.checksum.fl_str_mv |
bd3efa91386c1718a7f26a329fdcb468 4afdbb8c545fd630ea7db775da747b2f fda13080e892f3f68def2b8b70227968 9da0b6dfac957114c6a7714714b86306 0d49f26d4f922ddd70836a2024ad5850 22819b5eaff993a06ed4e8f1d1e19d03 1c994ef5f3d66271e71b312205144228 |
bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 MD5 MD5 MD5 |
repository.name.fl_str_mv |
Repositório Institucional da UFG - Universidade Federal de Goiás (UFG) |
repository.mail.fl_str_mv |
tasesdissertacoes.bc@ufg.br |
_version_ |
1798044336822157312 |