Geodesic
Ricci Solitons and Geometry of Four-dimensional Non-reductive Homogeneous Spaces
Canadian journal of mathematics, Tome 64 (2012) no. 4, pp. 778-804

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DOI

We study the geometry of non-reductive four-dimensional homogeneous spaces. In particular, after describing their Levi-Civita connection and curvature properties, we classify homogeneous Ricci solitons on these spaces, proving the existence of shrinking, expanding and steady examples. For all the non-trivial examples we find, the Ricci operator is diagonalizable.
DOI : 10.4153/CJM-2011-091-1
Mots-clés : 53C21, 53C50, 53C25, non-reductive homogeneous spaces, pseudo-Riemannianmetrics, Ricci solitons, Einsteinlike metrics 
Calvaruso, Giovanni; Fino, Anna. Ricci Solitons and Geometry of Four-dimensional Non-reductive Homogeneous Spaces. Canadian journal of mathematics, Tome 64 (2012) no. 4, pp. 778-804. doi: 10.4153/CJM-2011-091-1
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     journal = {Canadian journal of mathematics},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-091-1/}
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