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 if and only if the same is true of at times .
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