Gradiente ricci solitons e variedades de Einstein com métrica produto torcido

Detalhes bibliográficos
Autor(a) principal: Batista, Elismar Dias
Data de Publicação: 2016
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da UFG
Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/5693
Resumo: This work is based on the articles [26] and [27], where we studied Einstein manifolds and gradient Ricci soliton with twisted product structure. As a result, we prove the following: if M is an Einstein warped product space with nonpositive scalar curvature and compact base, then M is a Riemannian product space. Besides, we show that the Riemannian product Rp×F is a gradient Ricci soliton if and only if F is Ricci soliton gradient. Then, we show that the warped product R×f B is gradient Ricci solitons with f ′′ 6= 0, therefore F is Einstein. By using these results, we build nontrivial examples of gradient Ricci soliton where the fiber is either an Einstein manifold or a nontrivial gradient Ricci soliton.
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spelling Pina, Romildo da Silvahttp://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4782462D0Souza, Marcelo Almeida dehttp://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4797616Y0Pina, Romildo da SilvaSouza, Marcelo Almeida deaSantos, João Paulo doshttp://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4470771D1Batista, Elismar Dias2016-06-28T12:21:16Z2016-03-31BATISTA, E. D. Gradiente ricci solitons e variedades de Einstein com métrica produto torcido. 2016. 87 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2016.http://repositorio.bc.ufg.br/tede/handle/tede/5693This work is based on the articles [26] and [27], where we studied Einstein manifolds and gradient Ricci soliton with twisted product structure. As a result, we prove the following: if M is an Einstein warped product space with nonpositive scalar curvature and compact base, then M is a Riemannian product space. Besides, we show that the Riemannian product Rp×F is a gradient Ricci soliton if and only if F is Ricci soliton gradient. Then, we show that the warped product R×f B is gradient Ricci solitons with f ′′ 6= 0, therefore F is Einstein. By using these results, we build nontrivial examples of gradient Ricci soliton where the fiber is either an Einstein manifold or a nontrivial gradient Ricci soliton.Este trabalho está baseado nos artigos [26] e [27], onde estudamos Variedades de Einstein e gradiente Ricci solitons com estrutura de produto torcido. Provamos que: se M é um produto torcido Einstein com curvatura escalar não positiva e base compacta, então a função torção é constante, ou seja, o produto torcido é Riemanniano. Mostramos ainda que o produto Riemanniano Rp ×F é um gradiente Ricci soliton se e somente se F for gradiente Ricci soliton. Em seguida, mostramos que se o produto torcido R×f F for gradiente Ricci soliton com f ′′(t) 6= 0, então F é Einstein. Usando estes resultados construímos exemplos de gradiente Ricci soliton não trivial com a fibra sendo Einstein ou gradiente Ricci soliton não trivial. Finalmente consideramos o produto torcido Lorentziano sendo gradiente Ricci soliton e obtivemos critérios análogos ao Riemanniano para que F seja Einstein ou gradiente Ricci soliton.Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2016-06-15T19:51:42Z No. of bitstreams: 2 Dissertação - Elismar Dias Batista - 2016.pdf: 1518873 bytes, checksum: 8375db389a2056c5849ee168f5efa5ce (MD5) license_rdf: 19874 bytes, checksum: 38cb62ef53e6f513db2fb7e337df6485 (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-06-28T12:21:16Z (GMT) No. of bitstreams: 2 Dissertação - Elismar Dias Batista - 2016.pdf: 1518873 bytes, checksum: 8375db389a2056c5849ee168f5efa5ce (MD5) license_rdf: 19874 bytes, checksum: 38cb62ef53e6f513db2fb7e337df6485 (MD5)Made available in DSpace on 2016-06-28T12:21:16Z (GMT). No. of bitstreams: 2 Dissertação - Elismar Dias Batista - 2016.pdf: 1518873 bytes, checksum: 8375db389a2056c5849ee168f5efa5ce (MD5) license_rdf: 19874 bytes, checksum: 38cb62ef53e6f513db2fb7e337df6485 (MD5) Previous issue date: 2016-03-31Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESapplication/pdfporUniversidade Federal de GoiásPrograma de Pós-graduação em Matemática (IME)UFGBrasilInstituto de Matemática e Estatística - IME (RG)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessProduto torcidoVariedade de EinsteinGradiente ricci solitonWarped productEinstein manifoldsGradient ricci solitonsALGEBRA::GEOMETRIA ALGEBRICAGradiente ricci solitons e variedades de Einstein com métrica produto torcidoRicci solitons gradient and Einstein manifolds with warped product métricinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis6600717948137941247600600600600-4268777512335152015-18434713298420455952075167498588264571reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; 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dc.title.por.fl_str_mv Gradiente ricci solitons e variedades de Einstein com métrica produto torcido
dc.title.alternative.eng.fl_str_mv Ricci solitons gradient and Einstein manifolds with warped product métric
title Gradiente ricci solitons e variedades de Einstein com métrica produto torcido
spellingShingle Gradiente ricci solitons e variedades de Einstein com métrica produto torcido
Batista, Elismar Dias
Produto torcido
Variedade de Einstein
Gradiente ricci soliton
Warped product
Einstein manifolds
Gradient ricci solitons
ALGEBRA::GEOMETRIA ALGEBRICA
title_short Gradiente ricci solitons e variedades de Einstein com métrica produto torcido
title_full Gradiente ricci solitons e variedades de Einstein com métrica produto torcido
title_fullStr Gradiente ricci solitons e variedades de Einstein com métrica produto torcido
title_full_unstemmed Gradiente ricci solitons e variedades de Einstein com métrica produto torcido
title_sort Gradiente ricci solitons e variedades de Einstein com métrica produto torcido
author Batista, Elismar Dias
author_facet Batista, Elismar Dias
author_role author
dc.contributor.advisor1.fl_str_mv Pina, Romildo da Silva
dc.contributor.advisor1Lattes.fl_str_mv http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4782462D0
dc.contributor.advisor-co1.fl_str_mv Souza, Marcelo Almeida de
dc.contributor.advisor-co1Lattes.fl_str_mv http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4797616Y0
dc.contributor.referee1.fl_str_mv Pina, Romildo da Silva
dc.contributor.referee2.fl_str_mv Souza, Marcelo Almeida dea
dc.contributor.referee3.fl_str_mv Santos, João Paulo dos
dc.contributor.authorLattes.fl_str_mv http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4470771D1
dc.contributor.author.fl_str_mv Batista, Elismar Dias
contributor_str_mv Pina, Romildo da Silva
Souza, Marcelo Almeida de
Pina, Romildo da Silva
Souza, Marcelo Almeida dea
Santos, João Paulo dos
dc.subject.por.fl_str_mv Produto torcido
Variedade de Einstein
Gradiente ricci soliton
topic Produto torcido
Variedade de Einstein
Gradiente ricci soliton
Warped product
Einstein manifolds
Gradient ricci solitons
ALGEBRA::GEOMETRIA ALGEBRICA
dc.subject.eng.fl_str_mv Warped product
Einstein manifolds
Gradient ricci solitons
dc.subject.cnpq.fl_str_mv ALGEBRA::GEOMETRIA ALGEBRICA
description This work is based on the articles [26] and [27], where we studied Einstein manifolds and gradient Ricci soliton with twisted product structure. As a result, we prove the following: if M is an Einstein warped product space with nonpositive scalar curvature and compact base, then M is a Riemannian product space. Besides, we show that the Riemannian product Rp×F is a gradient Ricci soliton if and only if F is Ricci soliton gradient. Then, we show that the warped product R×f B is gradient Ricci solitons with f ′′ 6= 0, therefore F is Einstein. By using these results, we build nontrivial examples of gradient Ricci soliton where the fiber is either an Einstein manifold or a nontrivial gradient Ricci soliton.
publishDate 2016
dc.date.accessioned.fl_str_mv 2016-06-28T12:21:16Z
dc.date.issued.fl_str_mv 2016-03-31
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
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status_str publishedVersion
dc.identifier.citation.fl_str_mv BATISTA, E. D. Gradiente ricci solitons e variedades de Einstein com métrica produto torcido. 2016. 87 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2016.
dc.identifier.uri.fl_str_mv http://repositorio.bc.ufg.br/tede/handle/tede/5693
identifier_str_mv BATISTA, E. D. Gradiente ricci solitons e variedades de Einstein com métrica produto torcido. 2016. 87 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2016.
url http://repositorio.bc.ufg.br/tede/handle/tede/5693
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language por
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600
600
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dc.publisher.none.fl_str_mv Universidade Federal de Goiás
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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
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