Locally conformally flat ancient Ricci flows
Differential Geometry
2016-01-20 v5
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.
Keywords
Cite
@article{arxiv.1308.2374,
title = {Locally conformally flat ancient Ricci flows},
author = {Giovanni Catino and Carlo Mantegazza and Lorenzo Mazzieri},
journal= {arXiv preprint arXiv:1308.2374},
year = {2016}
}
Comments
Final version, to appear on Anal. PDE