Geodesic
On the Ricci curvature of three-dimensional metric Lie algebras
Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 1, pp. 57-67

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In this paper, we get a classification of possible values of the Ricci curvature signature of left invariant Riemannian metrics on three-dimensional Lie groups, that is a specification of some results of J. Milnor. As an auxiliary problem, we classify three-dimensional nonunimodular metric Lie algebras. 
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     author = {M. S. Chebarikov},
     title = {On the {Ricci} curvature of three-dimensional metric {Lie} algebras},
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M. S. Chebarikov. On the Ricci curvature of three-dimensional metric Lie algebras. Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 1, pp. 57-67. http://geodesic.mathdoc.fr/item/VMJ_2014_16_1_a6/