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G&T Monographs |
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A class of three-dimensional Ricci solitons
Paul Baird
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Geometry & Topology 13 (2009)
979–1015
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Abstract
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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.
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Keywords
Ricci soliton, semi-conformal map,
dynamical system
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Mathematical Subject Classification
Primary: 35Q51, 57M50
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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
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