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DOI: 10.23671/VNC.2014.1.7424

On the Ricci curvature of three-dimensional metric lie algebras

Chebarikov M. S.
Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 1.
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.
Keywords: homogeneous Riemannian manifold, Lie group, metric Lie algebra, three-dimensional Lie group, Ricci operator, eigenvalues of the Ricci operator, Ricci curvature
Language: Russian Download the full text  
For citation: Chebarikov M. S. On the Ricci curvature of three-dimensional metric lie algebras. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 16, no. 1, pp.57-67. DOI 10.23671/VNC.2014.1.7424
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