English

Ricci flow and the holonomy group

Differential Geometry 2011-05-19 v1

Abstract

We prove that the restricted holonomy group of a complete smooth solution to the Ricci flow of uniformly bounded curvature cannot spontaneously contract in finite time; it follows, then, from an earlier result of Hamilton that the holonomy group is exactly preserved by the equation. In particular, a solution to the Ricci flow may be K\"{a}hler or locally reducible (as a product) at t=Tt= T if and only if the same is true of g(t)g(t) at times tTt\leq T.

Keywords

Cite

@article{arxiv.1105.3722,
  title  = {Ricci flow and the holonomy group},
  author = {Brett L. Kotschwar},
  journal= {arXiv preprint arXiv:1105.3722},
  year   = {2011}
}

Comments

26 pages

R2 v1 2026-06-21T18:09:19.246Z