
Journal of Lie Theory 29 (2019), No. 4, 957968 Copyright Heldermann Verlag 2019 Left Invariant Ricci Solitons on ThreeDimensional Lie Groups Hamid R. Salimi Moghaddam Department of Mathematics, Faculty of Sciences, University of Isfahan, Isfahan 8174673441, Iran hr.salimi@sci.ui.ac.ir 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 threedimensional 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 threedimensional unimodular and nonunimodular Lie groups with left invariant Ricci solitons. Finally, for a unimodular solvable Lie group, the solution of the Ricci soliton equation is given, explicitly. Keywords: Ricci soliton, left invariant Riemannian metric, threedimensional Lie group. MSC: 22E60, 53C44, 53C21. [ Fulltextpdf (138 KB)] for subscribers only. 