Comptes Rendus
no. 21-22
Differential Geometry/Dynamical Systems
Liouville and geodesic Ricci solitons
[Solitons de Ricci de type Liouville et de type géodésique]

Présenté par : Étienne Ghys

Mircea Crasmareanu1
1 Faculty of Mathematics, “Al.I. Cuza” University, Iaşi, 700506, Romania
Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1305-1308.

Pour le fibré tangent d'une variété équipée d'une métrique pseudo-Riemannienne ayant un relèvement complet, deux classes de solitons de Ricci sont décrits : une famille à 1 paramètre de solitons de Ricci de type Liouville contractants si la variété de base est Ricci plate, et un soliton de Ricci de type géodésique nul si celle-ci est plate. Un résultat de non-existence de solitons de Ricci géodésiques est également obtenu dans le cas du fibré tangent d'une variété non plate.

On a tangent bundle endowed with a pseudo-Riemannian metric of complete lift type two classes of Ricci solitons are obtained: a 1-parameter family of shrinking Liouville Ricci solitons if the base manifold is Ricci flat and a steady geodesic Ricci soliton if the base manifold is flat. A nonexistence result of geodesic Ricci solitons for the tangent bundle of a non-flat space form is also provided.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.10.008
Mircea Crasmareanu 1

1 Faculty of Mathematics, “Al.I. Cuza” University, Iaşi, 700506, Romania 
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Mircea Crasmareanu. Liouville and geodesic Ricci solitons. Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1305-1308. doi : 10.1016/j.crma.2009.10.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.10.008/

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