A Structural Analysis of Warped Product Yamabe Gradient Solitons

Abstract

We investigate Yamabe gradient solitons, which are warped product manifolds. We show that the fiber of a nontrivial warped product Yamabe gradient soliton has constant scalar curvature. Based on this result, we obtain a specific class of warped products that cannot be nontrivial solitons. Furthermore, we derive estimates of the scalar curvature and the soliton function of warped product solitons.