Properties of Complete Noncompact Warped Product Gradient Yamabe Solitons
Differential Geometry
2019-04-18 v1
Abstract
In this paper, we look for properties of gradient Yamabe solitons on top of warped product manifolds. Utilizing the maximum principle, we find lower bound estimates for both the potential function of the soliton and the scalar curvature of the warped product. By slightly modifying Li-Yau's technique so that we can handle drifting Laplacians, we were able to find three different gradient estimates for the warping function, one for each sign of the scalar curvature of the fiber manifold. As an application, we exhibit a nonexistence theorem for gradient Yamabe solitons possessing certain metric properties on the base of the warped product.
Keywords
Cite
@article{arxiv.1904.08288,
title = {Properties of Complete Noncompact Warped Product Gradient Yamabe Solitons},
author = {Willian Isao Tokura and Levi Adriano and Romildo Pina and Marcelo Barboza},
journal= {arXiv preprint arXiv:1904.08288},
year = {2019}
}