Volume 13, issue 2 (2009)

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A class of three-dimensional Ricci solitons

Paul Baird

Geometry & Topology 13 (2009) 979–1015
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 whose metric factors then extends to a non-standard ${C}^{2}$ metric on ${S}^{2}$.

Keywords
Ricci soliton, semi-conformal map, dynamical system
Mathematical Subject Classification 2000
Primary: 57M50, 35Q51