Geodesic
Left Invariant Ricci Solitons on Three-Dimensional Lie Groups
Journal of Lie theory, Tome 29 (2019) no. 4, pp. 957-968
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We give a necessary and sufficient condition for an arbitrary real Lie group, to admit an algebraic Ricci soliton. As an application, we classify all algebraic Ricci solitons on three-dimensional real Lie groups, up to automorphism. This classification shows that, in dimension three, there exist a solvable Lie group and a simple Lie group such that they do not admit any algebraic Ricci soliton. Also it is shown that there exist three-dimensional unimodular and non-unimodular Lie groups with left invariant Ricci solitons. Finally, for a unimodular solvable Lie group, the solution of the Ricci soliton equation is given, explicitly.
Classification : 22E60, 53C44, 53C21
Mots-clés : Ricci soliton, left invariant Riemannian metric, three-dimensional Lie group 
@article{JLT_2019_29_4_JLT_2019_29_4_a3,
     author = {H. R. Salimi Moghaddam},
     title = {Left {Invariant} {Ricci} {Solitons} on {Three-Dimensional} {Lie} {Groups}},
     journal = {Journal of Lie theory},
     pages = {957--968},
     year = {2019},
     volume = {29},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2019_29_4_JLT_2019_29_4_a3/}
}
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H. R. Salimi Moghaddam. Left Invariant Ricci Solitons on Three-Dimensional Lie Groups. Journal of Lie theory, Tome 29 (2019) no. 4, pp. 957-968. http://geodesic.mathdoc.fr/item/JLT_2019_29_4_JLT_2019_29_4_a3/