Gradient Ricci almost soliton warped product
Differential Geometry
2021-05-04 v3
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.
Cite
@article{arxiv.1507.03038,
title = {Gradient Ricci almost soliton warped product},
author = {F. E. S. Feitosa and A. A. Freitas Filho and J. N. V. Gomes and R. S. Pina},
journal= {arXiv preprint arXiv:1507.03038},
year = {2021}
}
Comments
Final version which has been accepted for publication in Journal of Geometry and Physics