Abstract
We present the necessary and sufficient conditions for constructing gradient Ricci almost solitons that are realized as warped products. This will be done by means of Bishop–O’Neill’s formulas and a particular study of Riemannian manifolds satisfying a Ricci–Hessian type equation. We prove existence results and give an example of particular solutions of the PDEs that arise from our construction. We also prove a rigidity result for a gradient Ricci soliton Riemannian product in the class of gradient Ricci almost soliton warped products under some natural geometric assumptions on the warping function.
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