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Vladikavkazskii Matematicheskii Zhurnal, 2014, Volume 16, Number 1, Pages 57–67
(Mi vmj496)
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This article is cited in 3 scientific papers (total in 3 papers)
On the Ricci curvature of three-dimensional metric Lie algebras
M. S. Chebarikov
Rubtsovsk Industrial Intitute, Branch of Altai State Technical University, Rubtsovsk, Russia
Abstract:
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.
Key words:
homogeneous Riemannian manifold, Lie group, metric Lie algebra, three-dimensional Lie group, Ricci operator, eigenvalues of the Ricci operator, Ricci curvature.
Received: 02.04.2013
Citation:
M. S. Chebarikov, “On the Ricci curvature of three-dimensional metric Lie algebras”, Vladikavkaz. Mat. Zh., 16:1 (2014), 57–67
Linking options:
https://www.mathnet.ru/eng/vmj496 https://www.mathnet.ru/eng/vmj/v16/i1/p57
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| Abstract page: | 274 | | Full-text PDF : | 86 | | References: | 62 |
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