Variedades de Einstein e Ricci solitons com estrutura de produto torcido
Guardado en:
| Autor principal: | |
|---|---|
| Fecha de Publicación: | 2015 |
| Formato: | Doctoral thesis |
| Lenguaje: | por |
| Fuente: | Repositório Institucional da UFG |
| Download full: | http://repositorio.bc.ufg.br/tede/handle/tede/4958 |
Sumario: | In this thesis, primarily, we studied warped products semi-Riemannian Einstein manifolds. We considered the case in that the base is conformal to an n-dimensional pseudo- Euclidean space and invariant under the action of an (n 1)-dimensional translation group. We constructed new examples of Einstein warped products with zero Ricci curvature when the fiber is Ricci-flat. In particular, we obtain explicit solutions, in the case vacuum, for Einstein field equation. Furthermore, we consider M = B f F warped product gradient Ricci solitons. We proved that the potential function depends only on the base and the fiber F is necessarily Einstein manifold. We provide all such solutions in the case of steady gradient Ricci solitons when the base is conformal to an n-dimensional pseudo-Euclidean space, invariant under the action of an (n1)-dimensional translation group, and the fiber F is Ricci-flat. |
| _version_ | 1871426369113554944 |
|---|---|
| author | Sousa, Márcio Lemes de |
| author_browse | Sousa, Márcio Lemes de |
| author_facet | Sousa, Márcio Lemes de |
| author_role | author |
| bitstream.checksum.fl_str_mv | bd3efa91386c1718a7f26a329fdcb468 4afdbb8c545fd630ea7db775da747b2f ae2fe251842ade1134c5d9bb99b6eefe 9da0b6dfac957114c6a7714714b86306 1e9e1b9d216bad33d6b5919afa54a4e4 |
| bitstream.checksumAlgorithm.fl_str_mv | MD5 MD5 MD5 MD5 MD5 |
| bitstream.url.fl_str_mv | http://repositorio.bc.ufg.br/tede/bitstreams/f13bf308-c52a-490b-a64c-6a6d8261e490/download http://repositorio.bc.ufg.br/tede/bitstreams/ef371546-b647-420b-ad05-1d1129c18a56/download http://repositorio.bc.ufg.br/tede/bitstreams/1dc1562b-2c6c-4218-b831-12171047632b/download http://repositorio.bc.ufg.br/tede/bitstreams/e807b73b-46f9-42cb-b5b2-dacbf732d6c1/download http://repositorio.bc.ufg.br/tede/bitstreams/36e887f6-bf97-403d-bf24-25c8ebd569c2/download |
| collection | Repositório Institucional da UFG |
| contributor_str_mv | Pina, Romildo da Silva Pina, Romildo da Silva Ferraioli, Diego Catalano Qiaoling, Wang Corro, Armando Mauro Vasquez Adriano, Levi Rosa |
| dc.contributor.advisor1.fl_str_mv | Pina, Romildo da Silva |
| dc.contributor.advisor1Lattes.fl_str_mv | http://lattes.cnpq.br/2675728978857991 |
| dc.contributor.author.fl_str_mv | Sousa, Márcio Lemes de |
| dc.contributor.authorLattes.fl_str_mv | http://lattes.cnpq.br/1534708250926451 |
| dc.contributor.referee1.fl_str_mv | Pina, Romildo da Silva |
| dc.contributor.referee2.fl_str_mv | Ferraioli, Diego Catalano |
| dc.contributor.referee3.fl_str_mv | Qiaoling, Wang |
| dc.contributor.referee4.fl_str_mv | Corro, Armando Mauro Vasquez |
| dc.contributor.referee5.fl_str_mv | Adriano, Levi Rosa |
| dc.date.accessioned.fl_str_mv | 2015-11-30T07:35:41Z |
| dc.date.issued.fl_str_mv | 2015-07-03 |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.citation.fl_str_mv | SOUSA, Márcio Lemes de. Variedades de Einstein e Ricci solitons com estrutura de produto torcido. 2015. 63 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2015. |
| dc.identifier.uri.fl_str_mv | http://repositorio.bc.ufg.br/tede/handle/tede/4958 |
| dc.language.iso.fl_str_mv | por |
| dc.publisher.country.fl_str_mv | Brasil |
| dc.publisher.department.fl_str_mv | Instituto de Matemática e Estatística - IME (RG) |
| dc.publisher.initials.fl_str_mv | UFG |
| dc.publisher.none.fl_str_mv | Universidade Federal de Goiás |
| dc.publisher.program.fl_str_mv | Programa de Pós-graduação em Matemática (IME) |
| dc.relation.cnpq.fl_str_mv | -7090823417984401694 |
| dc.relation.confidence.fl_str_mv | 600 600 600 600 |
| dc.relation.department.fl_str_mv | -4268777512335152015 |
| dc.relation.program.fl_str_mv | 6600717948137941247 |
| dc.relation.sponsorship.fl_str_mv | 2075167498588264571 |
| dc.rights.driver.fl_str_mv | http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:Repositório Institucional da UFG instname:Universidade Federal de Goiás (UFG) instacron:UFG |
| dc.subject.cnpq.fl_str_mv | CIENCIAS EXATAS E DA TERRA::MATEMATICA |
| dc.subject.eng.fl_str_mv | Warped product Einstein manifolds Gradient ricci soliton |
| dc.subject.por.fl_str_mv | Produto torcido Variedades de Einstein Ricci soliton gradiente |
| dc.title.alternative.eng.fl_str_mv | Einstein manifolds and Ricci solitons with warped product structure |
| dc.title.por.fl_str_mv | Variedades de Einstein e Ricci solitons com estrutura de produto torcido |
| dc.type.driver.fl_str_mv | info:eu-repo/semantics/doctoralThesis |
| dc.type.status.fl_str_mv | info:eu-repo/semantics/publishedVersion |
| description | In this thesis, primarily, we studied warped products semi-Riemannian Einstein manifolds. We considered the case in that the base is conformal to an n-dimensional pseudo- Euclidean space and invariant under the action of an (n 1)-dimensional translation group. We constructed new examples of Einstein warped products with zero Ricci curvature when the fiber is Ricci-flat. In particular, we obtain explicit solutions, in the case vacuum, for Einstein field equation. Furthermore, we consider M = B f F warped product gradient Ricci solitons. We proved that the potential function depends only on the base and the fiber F is necessarily Einstein manifold. We provide all such solutions in the case of steady gradient Ricci solitons when the base is conformal to an n-dimensional pseudo-Euclidean space, invariant under the action of an (n1)-dimensional translation group, and the fiber F is Ricci-flat. |
| eu_rights_str_mv | openAccess |
| format | doctoralThesis |
| id | UFG-2_6a2e2bef89baabcb01954e2e88d641a1 |
| identifier_str_mv | SOUSA, Márcio Lemes de. Variedades de Einstein e Ricci solitons com estrutura de produto torcido. 2015. 63 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2015. |
| instacron_str | UFG |
| institution | UFG |
| instname_str | Universidade Federal de Goiás (UFG) |
| language | por |
| network_acronym_str | UFG-2 |
| network_name_str | Repositório Institucional da UFG |
| oai_identifier_str | oai:repositorio.bc.ufg.br:tede/4958 |
| publishDate | 2015 |
| publishDateSort | 2015 |
| publisher.none.fl_str_mv | Universidade Federal de Goiás |
| reponame_str | Repositório Institucional da UFG |
| repository.mail.fl_str_mv | grt.bc@ufg.br |
| repository.name.fl_str_mv | Repositório Institucional da UFG - Universidade Federal de Goiás (UFG) |
| repository_id_str | oai:repositorio.bc.ufg.br:tede/1234 |
| rights_invalid_str_mv | http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| spelling | Pina, Romildo da Silvahttp://lattes.cnpq.br/2675728978857991Pina, Romildo da SilvaFerraioli, Diego CatalanoQiaoling, WangCorro, Armando Mauro VasquezAdriano, Levi Rosahttp://lattes.cnpq.br/1534708250926451Sousa, Márcio Lemes de2015-11-30T07:35:41Z2015-07-03SOUSA, Márcio Lemes de. Variedades de Einstein e Ricci solitons com estrutura de produto torcido. 2015. 63 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2015.http://repositorio.bc.ufg.br/tede/handle/tede/4958In this thesis, primarily, we studied warped products semi-Riemannian Einstein manifolds. We considered the case in that the base is conformal to an n-dimensional pseudo- Euclidean space and invariant under the action of an (n 1)-dimensional translation group. We constructed new examples of Einstein warped products with zero Ricci curvature when the fiber is Ricci-flat. In particular, we obtain explicit solutions, in the case vacuum, for Einstein field equation. Furthermore, we consider M = B f F warped product gradient Ricci solitons. We proved that the potential function depends only on the base and the fiber F is necessarily Einstein manifold. We provide all such solutions in the case of steady gradient Ricci solitons when the base is conformal to an n-dimensional pseudo-Euclidean space, invariant under the action of an (n1)-dimensional translation group, and the fiber F is Ricci-flat.Nesta tese, primeiramente, estudamos variedades produto torcido semi-Riemannianas de Einstein, considerando-se o caso em que a base é conforme ao espaço pseudo- Euclidiano n -dimensional e invariante sob a ação de um grupo de translações (n1)-dimensional. Construímos novos exemplos de métricas produto torcido Einstein com curvatura de Ricci zero quando a fibra é Ricci -flat. Em particular, obtemos soluções explícitas, no caso de vácuo, para a equação de campo de Einstein. Em seguida, provamos que quando a variedade M = B f F é um Ricci soliton gradiente a função potencial depende apenas da base e a fibra F é necessariamente uma variedade de Einstein. Fornecemos todas as soluções, no caso de Ricci soliton gradiente steady, quando a base é conforme ao espaço pseudo- Euclidiano n -dimensional, invariante sob a ação de um grupo translações (n1) - dimensional, e a fibra F é Ricci -flat.Coordenação 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-nc-nd/4.0/info:eu-repo/semantics/openAccessProduto torcidoVariedades de EinsteinRicci soliton gradienteWarped productEinstein manifoldsGradient ricci solitonCIENCIAS EXATAS E DA TERRA::MATEMATICAVariedades de Einstein e Ricci solitons com estrutura de produto torcidoEinstein manifolds and Ricci solitons with warped product structureinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis6600717948137941247600600600600-4268777512335152015-70908234179844016942075167498588264571reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; charset=utf-82165http://repositorio.bc.ufg.br/tede/bitstreams/f13bf308-c52a-490b-a64c-6a6d8261e490/downloadbd3efa91386c1718a7f26a329fdcb468MD51CC-LICENSElicense_urllicense_urltext/plain; charset=utf-849http://repositorio.bc.ufg.br/tede/bitstreams/ef371546-b647-420b-ad05-1d1129c18a56/download4afdbb8c545fd630ea7db775da747b2fMD52license_textlicense_texttext/html; charset=utf-821468http://repositorio.bc.ufg.br/tede/bitstreams/1dc1562b-2c6c-4218-b831-12171047632b/downloadae2fe251842ade1134c5d9bb99b6eefeMD53license_rdflicense_rdfapplication/rdf+xml; charset=utf-823148http://repositorio.bc.ufg.br/tede/bitstreams/e807b73b-46f9-42cb-b5b2-dacbf732d6c1/download9da0b6dfac957114c6a7714714b86306MD54ORIGINALTese - Márcio Lemes de Sousa - 2015.pdfTese - Márcio Lemes de Sousa - 2015.pdfapplication/pdf2626758http://repositorio.bc.ufg.br/tede/bitstreams/36e887f6-bf97-403d-bf24-25c8ebd569c2/download1e9e1b9d216bad33d6b5919afa54a4e4MD55tede/49582015-11-30 05:35:41.944http://creativecommons.org/licenses/by-nc-nd/4.0/Acesso Abertoopen.accessoai:repositorio.bc.ufg.br:tede/4958http://repositorio.bc.ufg.br/tedeRepositório InstitucionalPUBhttps://repositorio.bc.ufg.br/tedeserver/oai/requestgrt.bc@ufg.bropendoar:oai:repositorio.bc.ufg.br:tede/12342015-11-30T07:35:41Repositório Institucional da UFG - Universidade Federal de Goiás (UFG)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 |
| spellingShingle | Variedades de Einstein e Ricci solitons com estrutura de produto torcido Sousa, Márcio Lemes de Produto torcido Variedades de Einstein Ricci soliton gradiente Warped product Einstein manifolds Gradient ricci soliton CIENCIAS EXATAS E DA TERRA::MATEMATICA |
| status_str | publishedVersion |
| title | Variedades de Einstein e Ricci solitons com estrutura de produto torcido |
| title_full | Variedades de Einstein e Ricci solitons com estrutura de produto torcido |
| title_fullStr | Variedades de Einstein e Ricci solitons com estrutura de produto torcido |
| title_full_unstemmed | Variedades de Einstein e Ricci solitons com estrutura de produto torcido |
| title_short | Variedades de Einstein e Ricci solitons com estrutura de produto torcido |
| title_sort | Variedades de Einstein e Ricci solitons com estrutura de produto torcido |
| topic | Produto torcido Variedades de Einstein Ricci soliton gradiente Warped product Einstein manifolds Gradient ricci soliton CIENCIAS EXATAS E DA TERRA::MATEMATICA |
| url | http://repositorio.bc.ufg.br/tede/handle/tede/4958 |