On rotationally invariant shrinking Ricci solitons

Brett Kotschwar

Vol. 236 (2008), No. 1, 73–88

DOI: 10.2140/pjm.2008.236.73

Abstract

We study the gradient Ricci shrinking soliton equation on rotationally symmetric manifolds of dimensions n ≥ 3 and prove that the only complete metrics on Sⁿ, ℝⁿ, and ℝ × Sⁿ⁻¹ that admit shrinking soliton structures are respectively the round, flat, and standard cylindrical metrics.

Keywords

Ricci solitons, Ricci flow

Mathematical Subject Classification 2000

Primary: 53C44

Secondary: 58J35

Milestones

Received: 1 September 2006

Revised: 21 January 2008

Accepted: 13 February 2008

Published: 1 May 2008