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Previous issue date: 2016-12-02 / In this work we introduce the notion of Ricci-Hessian type manifolds (M, g, cp, f, A) which is closely related to the construction of almost Ricci solitons realised as a warped product. We classify certain classes of the Ricci-Hessian type manifolds and derive some implications for almost Ricci solitons and generalised m-quasi-Einstein manifolds. We consider two complementary cases: V f and Vco are linearly independent in C'(M)- module X(M); and V f = hVso for some smooth function h on M. In the first case we show that the vector field VA belongs to the Ce•"(M)-module generated by V f and Vso, while in the second case, under additional hypothesis, the manifold is, around any regular point of f, locally isometric to a warped product. / Nesta tese apresentamos a noção de variedades tipo Ricci-Hessiano f, A) que está intrinsecamente relacionada à construção de quase-sólitons de Ricci que são produtos warped. Classificamos certas classes de variedades tipo Ricci-Hessiano e dedu-zimos algumas implicações para quase-sólitons de Ricci e variedades m-quasi-Einstein generalizadas. Consideramos dois casos complementares: V f e V40 são linearmente in-dependentes no C°°(M)-módulo X(M) e V f = hVg, para alguma função suave h sobre M. No primeiro caso mostramos que o campo vetorial VA pertence ao C°°(M)-módulo gerado por V f e Vyo, enquanto que no segundo caso, sob hipóteses adicionais, a varie-dade é, em uma vizinhança de qualquer ponto regular de f, localmente isométrica a um produto warped.
| Identifer | oai:union.ndltd.org:IBICT/oai:http://localhost:tede/5583 |
| Date | 02 December 2016 |
| Creators | Matos Neto, Manoel Vieira de |
| Contributors | Gomes, José Nazareno Vieira |
| Publisher | Universidade Federal do Amazonas, Programa de Pós-graduação em Matemática, UFAM, Brasil, Instituto de Ciências Exatas |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/doctoralThesis |
| Format | application/pdf |
| Source | reponame:Biblioteca Digital de Teses e Dissertações da UFAM, instname:Universidade Federal do Amazonas, instacron:UFAM |
| Rights | http://creativecommons.org/licenses/by-nc-nd/4.0/, info:eu-repo/semantics/openAccess |
| Relation | -7807118400798055458, 600, 500, -8156311678363143599 |
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