The evolution of the Weyl tensor under the Ricci flow (Q407786)

The authors work out the evolution equation under the Ricci flow of the Weyl tensor \(W\) of a Riemannian manifold. Then, they emphasize geometric consequences of the assumption that a manifold evolving by the Ricci flow is locally conformally flat at every time. In particular, they classify the ``Ricci solitons'' under the hypothesis of local conformal flatness.