A note on compact gradient Yamabe solitons

TL;DR

This paper provides a straightforward proof that compact Yamabe gradient solitons with dimension greater than two necessarily have constant scalar curvature.

Contribution

It offers a simple proof establishing that all compact Yamabe gradient solitons in higher dimensions have constant scalar curvature, simplifying previous understanding.

Findings

Compact Yamabe gradient solitons have constant scalar curvature for n>2

The proof simplifies previous arguments in the field

Enhances understanding of geometric properties of Yamabe solitons

Abstract

We will give a simple proof that the metric of any compact Yamabe gradient soliton (M,g) is a metric of constant scalar curvature when the dimension of the manifold n>2.