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Vladikavkaz. Mat. Zh., 2014, Volume 16, Number 1, Pages 57–67 (Mi vmj496)  

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.

Full text: PDF file (222 kB)
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Document Type: Article
UDC: 514.765
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

Citation in format AMSBIB
\Bibitem{Che14}
\by M.~S.~Chebarikov
\paper On the Ricci curvature of three-dimensional metric Lie algebras
\jour Vladikavkaz. Mat. Zh.
\yr 2014
\vol 16
\issue 1
\pages 57--67
\mathnet{http://mi.mathnet.ru/vmj496}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Kubo, K. Onda, Yu. Taketomi, H. Tamaru, “On the moduli spaces of left-invariant pseudo-Riemannian metrics on Lie groups”, Hiroshima Math. J., 46:3 (2016), 357–374  mathscinet  zmath  isi
    2. T. Hashinaga, H. Tamaru, K. Terada, “Milnor-type theorems for left-invariant Riemannian metrics on Lie groups”, J. Math. Soc. Jpn., 68:2 (2016), 669–684  crossref  mathscinet  zmath  isi  scopus
    3. H. Tamaru, “The space of left-invariant Riemannian metrics”, Geometry and Topology of Manifolds, Springer Proceedings in Mathematics & Statistics, 154, eds. A. Futaki, R. Miyaoka, Z. Tang, W. Zhang, Springer Japan, 2016, 315–326  crossref  mathscinet  zmath  isi  scopus
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