A note on gradient Ricci soliton warped metrics

TL;DR

This paper investigates gradient Ricci soliton warped metrics, establishing conditions for their triviality and nonexistence by analyzing Ricci-Hessian type base manifolds within warped product constructions.

Contribution

It provides new triviality and nonexistence results for gradient Ricci soliton warped metrics using Ricci-Hessian manifolds as the analytical framework.

Findings

Proves triviality of certain gradient Ricci soliton warped metrics.

Establishes nonexistence results under specific conditions.

Highlights the role of Ricci-Hessian manifolds in understanding soliton structures.

Abstract

In this note, we prove triviality and nonexistence results for gradient Ricci soliton warped metrics. The proofs stem from the construction of gradient Ricci solitons that are realized as warped products, from which we know that the base spaces of these products are Ricci-Hessian type manifolds. We study this latter class of manifolds as the most appropriate setting to prove our results.