Variedades quasi-Einstein com simetrias e generalizações
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFG |
Texto Completo: | http://repositorio.bc.ufg.br/tede/handle/tede/11141 |
Resumo: | In this work we study quasi-Einstein warped products and generalized quasi-Einstein manifolds locally conformally flat. We prove that in some quasi-Einstein semi-Riemannian warped product the fiber is necessarily an Einstein manifold. We provide all quasi-Einstein manifolds when r-Bakry-Émery tensor is null, the base is conformal to a n-dimensional pseudo-Euclidean space, invariant under the action of the (n-1)-dimensional translation group, the potential function depends only on the base and the fiber is Ricci-flat. As an application, we provide a family of Ricci-flat warped product whose base is not locally conformally flat. Considering generalized m-quasi-Einstein manifolds conformal to the pseudo-Euclidean space, we used an ansatz method to obtain the most general symmetry group of maximal dimension in which there are solutions to the system of equations that describe such manifolds. In addition, using the same method, we show that there is no different invariant of smaller dimension on a generalized m-quasi-Einstein manifold. |
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Pina, Romildo da Silvahttp://lattes.cnpq.br/2675728978857991Leandro Neto, BeneditoAdriano, Levi RosaCorro, Armando Mauro VasquezSantos, João Paulo dosFerraioli, Diego Catalanohttp://lattes.cnpq.br/5389521957571195Correia, Paula Gonçalves2021-03-05T14:53:17Z2021-03-05T14:53:17Z2021-12-05CORREIA, P. G. Variedades quasi-Einstein com simetrias e generalizações. 2021. 91 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2021.http://repositorio.bc.ufg.br/tede/handle/tede/11141In this work we study quasi-Einstein warped products and generalized quasi-Einstein manifolds locally conformally flat. We prove that in some quasi-Einstein semi-Riemannian warped product the fiber is necessarily an Einstein manifold. We provide all quasi-Einstein manifolds when r-Bakry-Émery tensor is null, the base is conformal to a n-dimensional pseudo-Euclidean space, invariant under the action of the (n-1)-dimensional translation group, the potential function depends only on the base and the fiber is Ricci-flat. As an application, we provide a family of Ricci-flat warped product whose base is not locally conformally flat. Considering generalized m-quasi-Einstein manifolds conformal to the pseudo-Euclidean space, we used an ansatz method to obtain the most general symmetry group of maximal dimension in which there are solutions to the system of equations that describe such manifolds. In addition, using the same method, we show that there is no different invariant of smaller dimension on a generalized m-quasi-Einstein manifold.Neste trabalho nós estudamos produtos torcidos quasi-Einstein e variedades quasi- Einstein generalizadas localmente conformemente planas. Provamos que em alguns produtos torcidos semi-Riemannianos quasi-Einstein a fibra é necessariamente uma variedade de Einstein. Nós obtemos todas as variedades quasi-Einstein quando o tensor r-Bakry-Émery é nulo, a base é conforme ao espaço pseudo-Euclidiano n-dimensional, a função potencial depende somente da base e a fibra é Ricci-flat, considerando invariância sob a ação do grupo de translação (n-1)-dimensional. A partir dessas variedades quasi-Einstein, obtemos uma família de produtos torcidos Ricci-flat cuja base não é localmente conformemente plana. Considerando variedades m-quasi-Einstein generalizadas conformes ao espaço pseudo-Euclidiano, utilizamos um método ansatz para obter o grupo de simetria mais geral de dimensão máxima no qual existem soluções para o sistema de equações que descreve tais variedades. Além disso, usando o mesmo método, mostramos que não existe invariante diferente de dimensão menor em uma variedade m-quasi-Einstein generalizada.Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2021-03-05T12:40:54Z No. of bitstreams: 2 license_rdf: 805 bytes, checksum: 4460e5956bc1d1639be9ae6146a50347 (MD5) Tese - Paula Gonçalves Correia Bonfim - 2021.pdf: 2268161 bytes, checksum: 9d9eb6881b9de9d0690966124a9dbe4e (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2021-03-05T14:53:17Z (GMT) No. of bitstreams: 2 license_rdf: 805 bytes, checksum: 4460e5956bc1d1639be9ae6146a50347 (MD5) Tese - Paula Gonçalves Correia Bonfim - 2021.pdf: 2268161 bytes, checksum: 9d9eb6881b9de9d0690966124a9dbe4e (MD5)Made available in DSpace on 2021-03-05T14:53:17Z (GMT). No. of bitstreams: 2 license_rdf: 805 bytes, checksum: 4460e5956bc1d1639be9ae6146a50347 (MD5) Tese - Paula Gonçalves Correia Bonfim - 2021.pdf: 2268161 bytes, checksum: 9d9eb6881b9de9d0690966124a9dbe4e (MD5) Previous issue date: 2021-12-05Coordenação 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 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessProduto torcido quasi-EinsteinVariedade quasi-Einstein generalizada localmente conformemente planaVariedade de EinsteinQuasi-Einstein warped productGeneralized quasi-Einstein manifold locally conformally flatEinstein manifoldCIENCIAS EXATAS E DA TERRA::MATEMATICAVariedades quasi-Einstein com simetrias e generalizaçõesQuasi-Einstein manifolds with symmetries and generalizationsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis66500500500500271871reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://repositorio.bc.ufg.br/tede/bitstreams/2d3b2f2e-c0c7-4cb1-b4c9-9a407a677806/download8a4605be74aa9ea9d79846c1fba20a33MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805http://repositorio.bc.ufg.br/tede/bitstreams/33f35a1d-38d5-44aa-be5f-6b7aa65f775b/download4460e5956bc1d1639be9ae6146a50347MD52ORIGINALTese - Paula Gonçalves Correia Bonfim - 2021.pdfTese - Paula Gonçalves Correia Bonfim - 2021.pdfapplication/pdf2268161http://repositorio.bc.ufg.br/tede/bitstreams/4c333988-e951-4bae-b2b2-73b7766a45ce/download9d9eb6881b9de9d0690966124a9dbe4eMD53tede/111412021-03-05 11:53:18.349http://creativecommons.org/licenses/by-nc-nd/4.0/Attribution-NonCommercial-NoDerivatives 4.0 Internationalopen.accessoai:repositorio.bc.ufg.br:tede/11141http://repositorio.bc.ufg.br/tedeRepositório InstitucionalPUBhttp://repositorio.bc.ufg.br/oai/requesttasesdissertacoes.bc@ufg.bropendoar:2021-03-05T14:53:18Repositório Institucional da UFG - Universidade Federal de Goiás (UFG)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 |
dc.title.pt_BR.fl_str_mv |
Variedades quasi-Einstein com simetrias e generalizações |
dc.title.alternative.eng.fl_str_mv |
Quasi-Einstein manifolds with symmetries and generalizations |
title |
Variedades quasi-Einstein com simetrias e generalizações |
spellingShingle |
Variedades quasi-Einstein com simetrias e generalizações Correia, Paula Gonçalves Produto torcido quasi-Einstein Variedade quasi-Einstein generalizada localmente conformemente plana Variedade de Einstein Quasi-Einstein warped product Generalized quasi-Einstein manifold locally conformally flat Einstein manifold CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Variedades quasi-Einstein com simetrias e generalizações |
title_full |
Variedades quasi-Einstein com simetrias e generalizações |
title_fullStr |
Variedades quasi-Einstein com simetrias e generalizações |
title_full_unstemmed |
Variedades quasi-Einstein com simetrias e generalizações |
title_sort |
Variedades quasi-Einstein com simetrias e generalizações |
author |
Correia, Paula Gonçalves |
author_facet |
Correia, Paula Gonçalves |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Pina, Romildo da Silva |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/2675728978857991 |
dc.contributor.referee1.fl_str_mv |
Leandro Neto, Benedito |
dc.contributor.referee2.fl_str_mv |
Adriano, Levi Rosa |
dc.contributor.referee3.fl_str_mv |
Corro, Armando Mauro Vasquez |
dc.contributor.referee4.fl_str_mv |
Santos, João Paulo dos |
dc.contributor.referee5.fl_str_mv |
Ferraioli, Diego Catalano |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/5389521957571195 |
dc.contributor.author.fl_str_mv |
Correia, Paula Gonçalves |
contributor_str_mv |
Pina, Romildo da Silva Leandro Neto, Benedito Adriano, Levi Rosa Corro, Armando Mauro Vasquez Santos, João Paulo dos Ferraioli, Diego Catalano |
dc.subject.por.fl_str_mv |
Produto torcido quasi-Einstein Variedade quasi-Einstein generalizada localmente conformemente plana Variedade de Einstein |
topic |
Produto torcido quasi-Einstein Variedade quasi-Einstein generalizada localmente conformemente plana Variedade de Einstein Quasi-Einstein warped product Generalized quasi-Einstein manifold locally conformally flat Einstein manifold CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Quasi-Einstein warped product Generalized quasi-Einstein manifold locally conformally flat Einstein manifold |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
In this work we study quasi-Einstein warped products and generalized quasi-Einstein manifolds locally conformally flat. We prove that in some quasi-Einstein semi-Riemannian warped product the fiber is necessarily an Einstein manifold. We provide all quasi-Einstein manifolds when r-Bakry-Émery tensor is null, the base is conformal to a n-dimensional pseudo-Euclidean space, invariant under the action of the (n-1)-dimensional translation group, the potential function depends only on the base and the fiber is Ricci-flat. As an application, we provide a family of Ricci-flat warped product whose base is not locally conformally flat. Considering generalized m-quasi-Einstein manifolds conformal to the pseudo-Euclidean space, we used an ansatz method to obtain the most general symmetry group of maximal dimension in which there are solutions to the system of equations that describe such manifolds. In addition, using the same method, we show that there is no different invariant of smaller dimension on a generalized m-quasi-Einstein manifold. |
publishDate |
2021 |
dc.date.accessioned.fl_str_mv |
2021-03-05T14:53:17Z |
dc.date.available.fl_str_mv |
2021-03-05T14:53:17Z |
dc.date.issued.fl_str_mv |
2021-12-05 |
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 |
CORREIA, P. G. Variedades quasi-Einstein com simetrias e generalizações. 2021. 91 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2021. |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/11141 |
identifier_str_mv |
CORREIA, P. G. Variedades quasi-Einstein com simetrias e generalizações. 2021. 91 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2021. |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/11141 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.program.fl_str_mv |
66 |
dc.relation.confidence.fl_str_mv |
500 500 500 500 |
dc.relation.department.fl_str_mv |
27 |
dc.relation.cnpq.fl_str_mv |
187 |
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1 |
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Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
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Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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openAccess |
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) |
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Universidade Federal de Goiás |
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