Gradient Ricci almost soliton warped product

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.

Final version which has been accepted for publication in Journal of Geometry and Physics

References in corpus (4)

• On the construction of gradient Ricci soliton warped product
• Ricci Almost Solitons on semi-Riemannian Warped Products
• On Warped product gradient Ricci Soliton
• Classification of base of warped product almost Ricci solitons

Cited by in corpus (6)

• Ricci Almost Solitons on semi-Riemannian Warped Products
• A note on gradient Ricci soliton warped metrics
• Geometric and analytic results for Einstein solitons
• Gradient Einstein-type warped products: rigidity, existence and nonexistence results via a nonlinear PDE
• Gradient Estimates on Warped Product Gradient Almost Ricci Solitons
• Classification of base of warped product almost Ricci solitons