Classification of base of warped product almost Ricci solitons
In this paper we study a Ricci-Hessian type manifold which is closely related to the construction of almost Ricci soliton realized as a warped product. We classify certain classes of the Ricci-Hessian type manifolds and derive some implications for almost Ricci solitons and generalized –quasi-Einstein manifolds. We consider two complementary cases: and are linearly independent in –module ; and for a smooth function on . In the first case we show that the vector field belongs to the –module generated by and , while in the second case, under additional hypothesis, the manifold is, around any regular point of , locally isometric to a warped product.