Submitted by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2017-03-14T14:39:41Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese - Manoel V. Matos Neto.pdf: 760344 bytes, checksum: 0f351aa7e31f3d221d36fb223b89f3a8 (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2017-03-14T14:40:12Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese - Manoel V. Matos Neto.pdf: 760344 bytes, checksum: 0f351aa7e31f3d221d36fb223b89f3a8 (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2017-03-14T14:40:26Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese - Manoel V. Matos Neto.pdf: 760344 bytes, checksum: 0f351aa7e31f3d221d36fb223b89f3a8 (MD5) / Made available in DSpace on 2017-03-14T14:40:26Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese - Manoel V. Matos Neto.pdf: 760344 bytes, checksum: 0f351aa7e31f3d221d36fb223b89f3a8 (MD5) 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.