A Structural Analysis of Warped Product Yamabe Gradient Solitons

TL;DR

This paper studies warped product Yamabe gradient solitons, revealing conditions under which their fibers have constant scalar curvature and identifying classes that cannot be nontrivial solitons, along with curvature estimates.

Contribution

It provides new insights into the structure of warped product Yamabe gradient solitons, including conditions for triviality and curvature bounds.

Findings

Fiber of nontrivial soliton has constant scalar curvature

Certain warped products cannot be nontrivial solitons

Derived estimates for scalar curvature and soliton function

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.