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Mat. Tr., 2010, Volume 13, Number 1, Pages 186–211 (Mi mt196)  

This article is cited in 6 scientific papers (total in 6 papers)

On the Ricci curvature of nonunimodular solvable metric Lie algebras of small dimension

M. S. Chebarykov

Rubtsovsk Industrial Intitute, Branch of Altai State Technical University, Rubtsovsk, Russia

Abstract: The Ricci curvature of solvable metric Lie algebras is studied. In particular, we prove that the Ricci operator of any metric nonunimodular solvable Lie algebra of dimension not exceeding 6 has at least two negative eigenvalues, that generalizes the known results.

Key words: homogeneous Riemannian manifold, Lie algebra, Lie group, left-invariant Riemannian metric, the Ricci curvature.

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English version:
Siberian Advances in Mathematics, 2011, 21:2, 81–99

Bibliographic databases:

Document Type: Article
UDC: 514.765
Received: 01.06.2009

Citation: M. S. Chebarykov, “On the Ricci curvature of nonunimodular solvable metric Lie algebras of small dimension”, Mat. Tr., 13:1 (2010), 186–211; Siberian Adv. Math., 21:2 (2011), 81–99

Citation in format AMSBIB
\Bibitem{Che10}
\by M.~S.~Chebarykov
\paper On the Ricci curvature of nonunimodular solvable metric Lie algebras of small dimension
\jour Mat. Tr.
\yr 2010
\vol 13
\issue 1
\pages 186--211
\mathnet{http://mi.mathnet.ru/mt196}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2682773}
\elib{http://elibrary.ru/item.asp?id=14646026}
\transl
\jour Siberian Adv. Math.
\yr 2011
\vol 21
\issue 2
\pages 81--99
\crossref{https://doi.org/10.3103/S1055134411020015}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Gladunova O.P., Rodionov E.D., Slavskii V.V., “Invariantnye tenzornye polya na gruppakh li maloi razmernosti”, Vestnik Kemerovskogo gosudarstvennogo universiteta, 2011, no. 3-1, 119–133  elib
    2. Yu. G. Nikonorov, M. S. Chebarykov, “The Ricci operator of completely solvable metric Lie algebras”, Siberian Adv. Math., 24:1 (2014), 18–25  mathnet  crossref  mathscinet  elib
    3. N. A. Abiev, “On the Ricci curvature of solvable metric lie algebras with two-step nilpotent derived algebras”, Siberian Adv. Math., 24:1 (2014), 1–11  mathnet  crossref  mathscinet
    4. M. S. Chebarykov, “O krivizne Richchi trekhmernykh metricheskikh algebr Li”, Vladikavk. matem. zhurn., 16:1 (2014), 57–67  mathnet
    5. Nikonorov Yu.G., “Negative Eigenvalues of the Ricci Operator of Solvable Metric Lie Algebras”, Geod. Dedic., 170:1 (2014), 119–133  crossref  mathscinet  zmath  isi  scopus
    6. Cairns G., Galic A.H., Nikolayevsky Yu., “Curvature Properties of Metric Nilpotent Lie Algebras Which Are Independent of Metric”, Ann. Glob. Anal. Geom., 51:3 (2017), 305–325  crossref  mathscinet  zmath  isi  scopus
  • Математические труды Siberian Advances in Mathematics
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