Classi cação da Base de Produtos Warped Quase-Solitons de Ricci

Abstract

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.