A note on gradient Ricci soliton warped metrics

In this note, we prove triviality and nonexistence results for gradient Ricci soliton warped metrics. The proofs stem from the construction of gradient Ricci solitons that are realized as warped products, from which we know that the base spaces of these products are Ricci–Hessian type manifolds. We study this latter class of manifolds as the most appropriate setting to prove our results.