English

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

R2 v1 2026-06-22T01:07:32.920Z