Geometry & Topology 13 (2009) 979–1015

DOI: 10.2140/gt.2009.13.979

Abstract

We describe a three-dimensional autonomous dynamical system, orbits of which determine the metrics of three-dimensional Ricci solitons. In general these are not of gradient type. A careful analysis of the asymptotic behaviour of orbits is required to establish whether the corresponding solitons are complete or otherwise. New examples are found. Special cases include soliton structures on surfaces. In particular, a non-gradient steady soliton is found on an infinite cover of S² ∖{two points} whose metric factors then extends to a non-standard C² metric on S².

Keywords

Ricci soliton, semi-conformal map, dynamical system

Mathematical Subject Classification

Primary: 35Q51, 57M50

References

Publication

Received: 27 August 2008
Revised: 17 December 2008
Accepted: 14 December 2008
Published: 12 January 2009
Proposed: Tobias Colding
Seconded: Ben Chow, Gang Tian

Authors