Gradiente ricci solitons e variedades de Einstein com métrica produto torcido
Autor(a) principal: | |
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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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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/5693ark:/38995/0013000001wcnThis 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 |
format |
masterThesis |
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 |
dc.identifier.dark.fl_str_mv |
ark:/38995/0013000001wcn |
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. ark:/38995/0013000001wcn |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/5693 |
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por |
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por |
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6600717948137941247 |
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600 600 600 600 |
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-4268777512335152015 |
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-1843471329842045595 |
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http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess |
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http://creativecommons.org/licenses/by/4.0/ |
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openAccess |
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Universidade Federal de Goiás |
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Programa de Pós-graduação em Matemática (IME) |
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UFG |
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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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