Unicidade dos solitons de Ricci gradiente estáveis

Detalhes bibliográficos
Autor(a) principal: Souza, Vítor Emanoel Resplandes de
Data de Publicação: 2022
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da UFG
dARK ID: ark:/38995/0013000001sw6
Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/12545
Resumo: We present the Ricci solitons, objects that appear as self-similar solutions of the Ricci flow. We show some properties and results related to these solitons. In addition, we study [2] and prove that a three-dimensional gradient steady Ricci soliton that is asymptotic to the Bryant soliton must be isometric to the Bryant soliton. This theorem was proved by Brendle [1], and more generally stated by Cao et al. However Cao states the result without any proof, thus, the ultimate goal of our research is to demonstrate the theorem stated by Cao by generalizing Brendle’s result to dimensions greater than or equal to 3.
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spelling Leandro Neto, Beneditohttp://lattes.cnpq.br/3393448440968708Leandro Neto, BeneditoBarboza, Marcelo BezerraSantos, João Paulo doshttp://lattes.cnpq.br/7689095129238571Souza, Vítor Emanoel Resplandes de2023-01-09T12:40:58Z2023-01-09T12:40:58Z2022-11-18SOUZA, V. E. R. Unicidade dos solitons de Ricci gradiente estáveis. 2022. 82 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2022.http://repositorio.bc.ufg.br/tede/handle/tede/12545ark:/38995/0013000001sw6We present the Ricci solitons, objects that appear as self-similar solutions of the Ricci flow. We show some properties and results related to these solitons. In addition, we study [2] and prove that a three-dimensional gradient steady Ricci soliton that is asymptotic to the Bryant soliton must be isometric to the Bryant soliton. This theorem was proved by Brendle [1], and more generally stated by Cao et al. However Cao states the result without any proof, thus, the ultimate goal of our research is to demonstrate the theorem stated by Cao by generalizing Brendle’s result to dimensions greater than or equal to 3.Neste trabalho apresentamos os sólitons de Ricci, objetos que surgem como soluções auto-similares do fluxo de Ricci. Mostraremos algumas propriedades e resultados relacionados a esses sólitons, além disso, provaremos que um sóliton de Ricci gradiente estável tridimensional que é assintótico ao sóliton de Bryant, deve ser isométrico ao sóliton de Bryant, esse teorema foi provado por Brendle. O mesmo teorema foi enunciado de maneira mais geral por Cao et al. para dimensão arbitrária. Nesse artigo, Cao et al. apenas enuncia o resultado sem uma demonstração, dessa forma, o objetivo final de nossa pesquisa é demonstrar o teorema enunciado por Cao et al. generalizando o resultado de Brendle para dimensões maiores ou iguais a 3.Submitted by Leandro Machado (leandromachado@ufg.br) on 2023-01-03T19:44:01Z No. of bitstreams: 2 Dissertação - Vítor Emanoel Resplandes de Souza - 2022.pdf: 1119056 bytes, checksum: d93c077e33a03572ab83b18a1e584e05 (MD5) license_rdf: 805 bytes, checksum: 4460e5956bc1d1639be9ae6146a50347 (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2023-01-09T12:40:57Z (GMT) No. of bitstreams: 2 Dissertação - Vítor Emanoel Resplandes de Souza - 2022.pdf: 1119056 bytes, checksum: d93c077e33a03572ab83b18a1e584e05 (MD5) license_rdf: 805 bytes, checksum: 4460e5956bc1d1639be9ae6146a50347 (MD5)Made available in DSpace on 2023-01-09T12:40:58Z (GMT). No. of bitstreams: 2 Dissertação - Vítor Emanoel Resplandes de Souza - 2022.pdf: 1119056 bytes, checksum: d93c077e33a03572ab83b18a1e584e05 (MD5) license_rdf: 805 bytes, checksum: 4460e5956bc1d1639be9ae6146a50347 (MD5) Previous issue date: 2022-11-18Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESporUniversidade Federal de GoiásPrograma de Pós-graduação em Matemática (IME)UFGBrasilInstituto de Matemática e Estatística - IME (RMG)Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessSoliton de RicciEstávelSóliton de BryantRicci slitonSteadyBryant solitonCIENCIAS EXATAS E DA TERRA::MATEMATICAUnicidade dos solitons de Ricci gradiente estáveisUniqueness of gradient steady Ricci solitonsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis70500500500500271871reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://repositorio.bc.ufg.br/tede/bitstreams/3f489386-2d9b-44e6-bd18-5a9af36da28b/download8a4605be74aa9ea9d79846c1fba20a33MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805http://repositorio.bc.ufg.br/tede/bitstreams/de281049-ee73-4b53-9ea8-b6b1e3ed6827/download4460e5956bc1d1639be9ae6146a50347MD52ORIGINALDissertação - Vítor Emanoel Resplandes de Souza - 2022.pdfDissertação - Vítor Emanoel Resplandes de Souza - 2022.pdfapplication/pdf1119056http://repositorio.bc.ufg.br/tede/bitstreams/1e0dc688-81d1-4c5e-8acd-a0ac5403ad5c/downloadd93c077e33a03572ab83b18a1e584e05MD53tede/125452023-01-09 09:40:58.898http://creativecommons.org/licenses/by-nc-nd/4.0/Attribution-NonCommercial-NoDerivatives 4.0 Internationalopen.accessoai:repositorio.bc.ufg.br:tede/12545http://repositorio.bc.ufg.br/tedeRepositório InstitucionalPUBhttp://repositorio.bc.ufg.br/oai/requesttasesdissertacoes.bc@ufg.bropendoar:2023-01-09T12:40:58Repositório Institucional da UFG - Universidade Federal de Goiás (UFG)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
dc.title.pt_BR.fl_str_mv Unicidade dos solitons de Ricci gradiente estáveis
dc.title.alternative.eng.fl_str_mv Uniqueness of gradient steady Ricci solitons
title Unicidade dos solitons de Ricci gradiente estáveis
spellingShingle Unicidade dos solitons de Ricci gradiente estáveis
Souza, Vítor Emanoel Resplandes de
Soliton de Ricci
Estável
Sóliton de Bryant
Ricci sliton
Steady
Bryant soliton
CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Unicidade dos solitons de Ricci gradiente estáveis
title_full Unicidade dos solitons de Ricci gradiente estáveis
title_fullStr Unicidade dos solitons de Ricci gradiente estáveis
title_full_unstemmed Unicidade dos solitons de Ricci gradiente estáveis
title_sort Unicidade dos solitons de Ricci gradiente estáveis
author Souza, Vítor Emanoel Resplandes de
author_facet Souza, Vítor Emanoel Resplandes de
author_role author
dc.contributor.advisor1.fl_str_mv Leandro Neto, Benedito
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/3393448440968708
dc.contributor.referee1.fl_str_mv Leandro Neto, Benedito
dc.contributor.referee2.fl_str_mv Barboza, Marcelo Bezerra
dc.contributor.referee3.fl_str_mv Santos, João Paulo dos
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/7689095129238571
dc.contributor.author.fl_str_mv Souza, Vítor Emanoel Resplandes de
contributor_str_mv Leandro Neto, Benedito
Leandro Neto, Benedito
Barboza, Marcelo Bezerra
Santos, João Paulo dos
dc.subject.por.fl_str_mv Soliton de Ricci
Estável
Sóliton de Bryant
topic Soliton de Ricci
Estável
Sóliton de Bryant
Ricci sliton
Steady
Bryant soliton
CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv Ricci sliton
Steady
Bryant soliton
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA
description We present the Ricci solitons, objects that appear as self-similar solutions of the Ricci flow. We show some properties and results related to these solitons. In addition, we study [2] and prove that a three-dimensional gradient steady Ricci soliton that is asymptotic to the Bryant soliton must be isometric to the Bryant soliton. This theorem was proved by Brendle [1], and more generally stated by Cao et al. However Cao states the result without any proof, thus, the ultimate goal of our research is to demonstrate the theorem stated by Cao by generalizing Brendle’s result to dimensions greater than or equal to 3.
publishDate 2022
dc.date.issued.fl_str_mv 2022-11-18
dc.date.accessioned.fl_str_mv 2023-01-09T12:40:58Z
dc.date.available.fl_str_mv 2023-01-09T12:40:58Z
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 SOUZA, V. E. R. Unicidade dos solitons de Ricci gradiente estáveis. 2022. 82 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2022.
dc.identifier.uri.fl_str_mv http://repositorio.bc.ufg.br/tede/handle/tede/12545
dc.identifier.dark.fl_str_mv ark:/38995/0013000001sw6
identifier_str_mv SOUZA, V. E. R. Unicidade dos solitons de Ricci gradiente estáveis. 2022. 82 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2022.
ark:/38995/0013000001sw6
url http://repositorio.bc.ufg.br/tede/handle/tede/12545
dc.language.iso.fl_str_mv por
language por
dc.relation.program.fl_str_mv 70
dc.relation.confidence.fl_str_mv 500
500
500
500
dc.relation.department.fl_str_mv 27
dc.relation.cnpq.fl_str_mv 187
dc.relation.sponsorship.fl_str_mv 1
dc.rights.driver.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv 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 (RMG)
publisher.none.fl_str_mv Universidade Federal de Goiás
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFG
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reponame_str Repositório Institucional da UFG
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