On warped product manifolds satisfying Ricci-Hessian class type equations

We deal with a study of warped product manifold which is also a generalized quasi Einstein manifold. Then, we investigate the relationships between such warped products and certain manifolds that provide some Ricci-Hessian type equations, such as Ricmf = ?g for some smooth function ?, where Ricmf denotes the m-Bakery-Emery Ricci tensor. Finally, we obtain some rigidity conditions for such manifolds. nema