A class of three-dimensional Ricci solitons

Baird, Paul

doi:10.2140/gt.2009.13.979

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A class of three-dimensional Ricci solitons

Paul Baird

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 $S^{2} ∖ {two points}$ 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

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

Paul Baird
Département de Mathématiques Université de Bretagne Occidentale 6 av. Victor Le Gorgeu – CS 93837 29238 Brest Cedex France

Volume 13, issue 2 (2009)