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Mat. Tr., 2012, Volume 15, Number 2, Pages 146–158 (Mi mt244)  

This article is cited in 2 scientific papers (total in 2 papers)

The Ricci operator of completely solvable metric Lie algebras

Yu. G. Nikonorova, M. S. Chebarykovb

a South Mathematical Institute of VSC RAS, Vladikavkaz, Russia
b Rubtsovsk Industrial Intitute, Branch of Altai State Technical University, Rubtsovsk, Russia

Abstract: We study the Ricci curvature of completely solvable metric Lie algebras. In particular, we prove that the Ricci operator of every completely solvable nonunimodular or every noncommutative nilpotent metric Lie algebra has at least two negative eigenvalues.

Key words: nonhomogeneous Riemannian manifolds, Lie group and algebras, completely solvable Lie algebras, left-invariant Riemannian metrics, Ricci curvature.

Full text: PDF file (214 kB)
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English version:
Siberian Advances in Mathematics, 2014, 24:1, 18–25

Bibliographic databases:

Document Type: Article
UDC: 514.765
Received: 07.11.2011

Citation: Yu. G. Nikonorov, M. S. Chebarykov, “The Ricci operator of completely solvable metric Lie algebras”, Mat. Tr., 15:2 (2012), 146–158; Siberian Adv. Math., 24:1 (2014), 18–25

Citation in format AMSBIB
\Bibitem{NikChe12}
\by Yu.~G.~Nikonorov, M.~S.~Chebarykov
\paper The Ricci operator of completely solvable metric Lie algebras
\jour Mat. Tr.
\yr 2012
\vol 15
\issue 2
\pages 146--158
\mathnet{http://mi.mathnet.ru/mt244}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3074460}
\elib{http://elibrary.ru/item.asp?id=18076208}
\transl
\jour Siberian Adv. Math.
\yr 2014
\vol 24
\issue 1
\pages 18--25
\crossref{https://doi.org/10.3103/S1055134414010039}


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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. 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
    2. 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
  • Математические труды Siberian Advances in Mathematics
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