Dimension reduction under the Ricci flow on manifolds with nonnegative curvature operator

Xiaodong Cao

Vol. 232 (2007), No. 2, 263–268

DOI: 10.2140/pjm.2007.232.263

Abstract

In this paper, we study the dilation limit of solutions to the Ricci flow on manifolds with nonnegative curvature operator. We first show that such a dilation limit must be a product of a compact ancient Type I solution of the Ricci flow with flat factors. Then we show that, under the Type I normalized Ricci flow, the compact factor has a subsequence converging to a Ricci soliton.

Keywords

Ricci flow

Mathematical Subject Classification 2000

Primary: 53C44

Milestones

Received: 4 July 2006

Revised: 2 December 2006

Accepted: 22 December 2006

Published: 1 October 2007