On noncompact warped product Ricci solitons
Differential Geometry
2022-03-15 v1
Abstract
The goal of this article is to investigate complete noncompact warped product gradient Ricci solitons. Nonexistence results, estimates for the warping function and for its gradient are proven. When the soliton is steady or expanding these nonexistence results generalize to a broader context certain pde estimates and rigidity obtained when studying warped product Einstein manifolds. When the soliton is shrinking, it is presented a nonexistence theorem with no counterpart in the Einstein case, which is proved using properties of the first eigenvalue of a weighted Laplacian.
Keywords
Cite
@article{arxiv.2203.06441,
title = {On noncompact warped product Ricci solitons},
author = {Valter Borges},
journal= {arXiv preprint arXiv:2203.06441},
year = {2022}
}