Hipersuperfícies conformemente euclidianas com curvatura média ou escalar constante
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/8794 |
Resumo: | In this work we study conformally flat hypersurfaces f: M3 ^ Q4(c) with three distinct principal curvatures in a space form with constant sectional curvature c, under the assumption that either its mean curvature H or its scalar curvature S is constant. In case H is constant, first we extend to any c G R a theorem due to Defever when c = 0 and show that there is no such hypersurface if H = 0. Our main results are for the minimal case H = 0. If c = 0, we prove that f (M3) is an open subset of a generalized cone over a Clifford torus in an umbilical hypersurface Q4(c) C Q4(c), c > 0, with c > c if c > 0. For c = 0, we show that, besides the cone over the Clifford torus in S3 C R4, there exists precisely a one-parameter family of (congruence classes of) minimal isometric immersions f: M3 ^ R4 with three distinct principal curvatures of simply-connected conformally flat Riemannian manifolds. Assuming S to be constant, we only study the case c = 0. We prove that f (M3) is an open subset of a cylinder over a surface of nonzero constant Gauss curvature in R3. |
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Rei Filho, Carlos Gonçalves doFigueiredo Junior, Ruy Tojeiro dehttp://lattes.cnpq.br/9930999514347198http://lattes.cnpq.br/5461170290751462a9725836-76be-4585-b40c-402818cc7ff82017-05-31T19:42:46Z2017-05-31T19:42:46Z2016-11-10REI FILHO, Carlos Gonçalves do. Hipersuperfícies conformemente euclidianas com curvatura média ou escalar constante. 2016. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2016. Disponível em: https://repositorio.ufscar.br/handle/ufscar/8794.https://repositorio.ufscar.br/handle/ufscar/8794In this work we study conformally flat hypersurfaces f: M3 ^ Q4(c) with three distinct principal curvatures in a space form with constant sectional curvature c, under the assumption that either its mean curvature H or its scalar curvature S is constant. In case H is constant, first we extend to any c G R a theorem due to Defever when c = 0 and show that there is no such hypersurface if H = 0. Our main results are for the minimal case H = 0. If c = 0, we prove that f (M3) is an open subset of a generalized cone over a Clifford torus in an umbilical hypersurface Q4(c) C Q4(c), c > 0, with c > c if c > 0. For c = 0, we show that, besides the cone over the Clifford torus in S3 C R4, there exists precisely a one-parameter family of (congruence classes of) minimal isometric immersions f: M3 ^ R4 with three distinct principal curvatures of simply-connected conformally flat Riemannian manifolds. Assuming S to be constant, we only study the case c = 0. We prove that f (M3) is an open subset of a cylinder over a surface of nonzero constant Gauss curvature in R3.Nesta tese estudamos hipersuperfícies conformemente euclidianas f : M3 ^ Q4(c), com três curvaturas principais distintas e curvatura média H ou curvatura escalar S constante, em formas espaciais com curvatura seccional c. No caso em que a curvatura média H é constante, inicialmente estendemos para c arbitrário um resultado provado por Defever [10] quando c =0 e mostramos que uma tal hipersuperfície não existe se H = 0. Nossos principais resultados são para o caso mínimo H = 0. Se c = 0, mostramos que f (M3) é um subconjunto aberto de um cone generalizado sobre um toro de Clifford em uma hipersuperfície umbílica Q3(c) C Q4(c), c > 0, com c > c se c > 0. Para c = 0, mostramos que, além do cone sobre o toro de Clifford em S3 C R4, existe precisamente uma família a 1-parâmetro de hipersuperfícies conformemente euclidianas com três curvaturas principais distintas duas a duas não congruentes, sendo o cone sobre o toro de Clifford o elemento singular da família. No caso em que a curvatura escalar é constante, estudamos apenas o caso c = 0. Mostramos, nesse caso, que f (M3) é um subconjunto aberto de um cilindro sobre uma superfície de curvatura Gaussiana constante do espaço euclidiano R3.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)porUniversidade Federal de São CarlosCâmpus São CarlosPrograma de Pós-Graduação em Matemática - PPGMUFSCarHipersuperfícies conformemente euclidianasHipersuperfícies mínimasCurvaturas principais distintasConformally flat hypersurfacesMinimal hypersurfacesDistinct principal curvaturesConstant meanCIENCIAS EXATAS E DA TERRA::MATEMATICACIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIAHipersuperfícies conformemente euclidianas com curvatura média ou escalar constanteinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisOnline60060027fd6011-41f1-45f6-8dbf-fc4a2dd73c9binfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALTeseCGRF.pdfTeseCGRF.pdfapplication/pdf1149604https://repositorio.ufscar.br/bitstream/ufscar/8794/1/TeseCGRF.pdf8b0a42d65883e0af42693ac90b36059aMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81957https://repositorio.ufscar.br/bitstream/ufscar/8794/2/license.txtae0398b6f8b235e40ad82cba6c50031dMD52TEXTTeseCGRF.pdf.txtTeseCGRF.pdf.txtExtracted texttext/plain173936https://repositorio.ufscar.br/bitstream/ufscar/8794/3/TeseCGRF.pdf.txt029d2bdfff5d1e4b34477393e66e133fMD53THUMBNAILTeseCGRF.pdf.jpgTeseCGRF.pdf.jpgIM Thumbnailimage/jpeg6919https://repositorio.ufscar.br/bitstream/ufscar/8794/4/TeseCGRF.pdf.jpg04c5719eb35463c614a3e743da47d648MD54ufscar/87942023-09-18 18:31:24.338oai:repositorio.ufscar.br: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Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:31:24Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.por.fl_str_mv |
Hipersuperfícies conformemente euclidianas com curvatura média ou escalar constante |
title |
Hipersuperfícies conformemente euclidianas com curvatura média ou escalar constante |
spellingShingle |
Hipersuperfícies conformemente euclidianas com curvatura média ou escalar constante Rei Filho, Carlos Gonçalves do Hipersuperfícies conformemente euclidianas Hipersuperfícies mínimas Curvaturas principais distintas Conformally flat hypersurfaces Minimal hypersurfaces Distinct principal curvatures Constant mean CIENCIAS EXATAS E DA TERRA::MATEMATICA CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA |
title_short |
Hipersuperfícies conformemente euclidianas com curvatura média ou escalar constante |
title_full |
Hipersuperfícies conformemente euclidianas com curvatura média ou escalar constante |
title_fullStr |
Hipersuperfícies conformemente euclidianas com curvatura média ou escalar constante |
title_full_unstemmed |
Hipersuperfícies conformemente euclidianas com curvatura média ou escalar constante |
title_sort |
Hipersuperfícies conformemente euclidianas com curvatura média ou escalar constante |
author |
Rei Filho, Carlos Gonçalves do |
author_facet |
Rei Filho, Carlos Gonçalves do |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/5461170290751462 |
dc.contributor.author.fl_str_mv |
Rei Filho, Carlos Gonçalves do |
dc.contributor.advisor1.fl_str_mv |
Figueiredo Junior, Ruy Tojeiro de |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/9930999514347198 |
dc.contributor.authorID.fl_str_mv |
a9725836-76be-4585-b40c-402818cc7ff8 |
contributor_str_mv |
Figueiredo Junior, Ruy Tojeiro de |
dc.subject.por.fl_str_mv |
Hipersuperfícies conformemente euclidianas Hipersuperfícies mínimas Curvaturas principais distintas |
topic |
Hipersuperfícies conformemente euclidianas Hipersuperfícies mínimas Curvaturas principais distintas Conformally flat hypersurfaces Minimal hypersurfaces Distinct principal curvatures Constant mean CIENCIAS EXATAS E DA TERRA::MATEMATICA CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA |
dc.subject.eng.fl_str_mv |
Conformally flat hypersurfaces Minimal hypersurfaces Distinct principal curvatures Constant mean |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA |
description |
In this work we study conformally flat hypersurfaces f: M3 ^ Q4(c) with three distinct principal curvatures in a space form with constant sectional curvature c, under the assumption that either its mean curvature H or its scalar curvature S is constant. In case H is constant, first we extend to any c G R a theorem due to Defever when c = 0 and show that there is no such hypersurface if H = 0. Our main results are for the minimal case H = 0. If c = 0, we prove that f (M3) is an open subset of a generalized cone over a Clifford torus in an umbilical hypersurface Q4(c) C Q4(c), c > 0, with c > c if c > 0. For c = 0, we show that, besides the cone over the Clifford torus in S3 C R4, there exists precisely a one-parameter family of (congruence classes of) minimal isometric immersions f: M3 ^ R4 with three distinct principal curvatures of simply-connected conformally flat Riemannian manifolds. Assuming S to be constant, we only study the case c = 0. We prove that f (M3) is an open subset of a cylinder over a surface of nonzero constant Gauss curvature in R3. |
publishDate |
2016 |
dc.date.issued.fl_str_mv |
2016-11-10 |
dc.date.accessioned.fl_str_mv |
2017-05-31T19:42:46Z |
dc.date.available.fl_str_mv |
2017-05-31T19:42:46Z |
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 |
REI FILHO, Carlos Gonçalves do. Hipersuperfícies conformemente euclidianas com curvatura média ou escalar constante. 2016. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2016. Disponível em: https://repositorio.ufscar.br/handle/ufscar/8794. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/8794 |
identifier_str_mv |
REI FILHO, Carlos Gonçalves do. Hipersuperfícies conformemente euclidianas com curvatura média ou escalar constante. 2016. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2016. Disponível em: https://repositorio.ufscar.br/handle/ufscar/8794. |
url |
https://repositorio.ufscar.br/handle/ufscar/8794 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.confidence.fl_str_mv |
600 600 |
dc.relation.authority.fl_str_mv |
27fd6011-41f1-45f6-8dbf-fc4a2dd73c9b |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus São Carlos |
dc.publisher.program.fl_str_mv |
Programa de Pós-Graduação em Matemática - PPGM |
dc.publisher.initials.fl_str_mv |
UFSCar |
publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus São Carlos |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFSCAR instname:Universidade Federal de São Carlos (UFSCAR) instacron:UFSCAR |
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UFSCAR |
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UFSCAR |
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Repositório Institucional da UFSCAR |
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