Gradient shrinking solitons with vanishing Weyl tensor

Zhu-Hong Zhang

Vol. 242 (2009), No. 1, 189–200

DOI: 10.2140/pjm.2009.242.189

Abstract

We will give a local version of the Hamilton–Ivey-type pinching estimate of the gradient shrinking soliton with vanishing Weyl tensor, and then give a complete classification of gradient shrinking solitons with vanishing Weyl tensor.

Keywords

gradient Ricci soliton, vanishing Weyl tensor, Hamilton–Ivey pinching estimate

Mathematical Subject Classification 2000

Primary: 53C44

Milestones

Received: 21 September 2008

Revised: 17 January 2009

Accepted: 19 January 2009

Published: 1 September 2009