Locally conformally flat ancient Ricci flows

Abstract

We show that any locally conformally flat ancient solution to the Ricci flow must be rotationally symmetric. As a by-product, we prove that any locally conformally flat Ricci soliton is a gradient soliton in the shrinking and steady cases as well as in the expanding case, provided the soliton has nonnegative curvature.

Final version, to appear on Anal. PDE

References in corpus (3)

• Evolution of the Weyl Tensor under the Ricci Flow
• Ancient solutions to the Ricci flow with pinched curvature
• A local version of Bando's theorem on the real-analyticity of solutions to the Ricci flow

Cited by in corpus (3)

• Ricci Almost Solitons on semi-Riemannian Warped Products
• Rotationally symmetric Ricci flow on ${\mathbb{R}}^{n+1}$
• Cohomogeneity two Ricci solitons with sub-Euclidean volume