A nongradient Ricci almost soliton

TL;DR

This paper introduces a new construction method and explicit example of nongradient Ricci almost solitons in warped products, along with a rigidity result for the Gaussian soliton, expanding understanding of Ricci soliton structures.

Contribution

It provides the first explicit example and construction method for nongradient Ricci almost solitons in warped products, and establishes a rigidity result for Gaussian solitons.

Findings

Constructed explicit nongradient Ricci almost soliton example

Developed a new method for constructing such solitons

Proved a rigidity result for Gaussian solitons

Abstract

In this note, we present a construction method and an explicit example of nongradient (expanding or indefinite) Ricci almost soliton in a warped product. Moreover, we show a rigidity result for the Gaussian soliton.