Evolution of the Weyl Tensor under the Ricci Flow

TL;DR

This paper derives how the Weyl tensor changes under Ricci flow and explores implications for classifying locally conformally flat Ricci solitons.

Contribution

It provides the evolution equation of the Weyl tensor under Ricci flow and discusses its impact on the classification of certain Ricci solitons.

Findings

Derived the evolution equation of the Weyl tensor under Ricci flow

Discussed consequences for classifying locally conformally flat Ricci solitons

Contributed to understanding geometric evolution in Riemannian manifolds

Abstract

We compute the evolution equation of the Weyl tensor under the Ricci flow of a Riemannian manifold and we discuss some consequences for the classification of locally conformally flat Ricci solitons.