Geodesic
A class of three-dimensional Ricci solitons
Baird, Paul1
1 Département de Mathématiques, Université de Bretagne Occidentale, 6 av. Victor Le Gorgeu – CS 93837, 29238 Brest Cedex, France
Geometry & topology, Tome 13 (2009) no. 2, pp. 979-1015.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/gt.2009.13.979
Keywords: Ricci soliton, semi-conformal map, dynamical system

Baird, Paul 1

1 Département de Mathématiques, Université de Bretagne Occidentale, 6 av. Victor Le Gorgeu – CS 93837, 29238 Brest Cedex, France 
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Baird, Paul. A class of three-dimensional Ricci solitons. Geometry & topology, Tome 13 (2009) no. 2, pp. 979-1015. doi : 10.2140/gt.2009.13.979. http://geodesic.mathdoc.fr/articles/10.2140/gt.2009.13.979/

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