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The Ricci operator of completely solvable metric lie algebras

Abstract

We study the Ricci curvature of completely solvablemetric 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.

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Correspondence to M. S. Chebarykov.

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Original Russian Text © M.S. Chebarykov and Yu.G. Nikonorov, 2012, published in Matematicheskie Trudy, 2012, Vol. 15, No. 2, pp. 146–158.

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Chebarykov, M.S., Nikonorov, Y.G. The Ricci operator of completely solvable metric lie algebras. Sib. Adv. Math. 24, 18–25 (2014). https://doi.org/10.3103/S1055134414010039

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Keywords

  • nonhomogeneous Riemannian manifolds
  • Lie group and algebras
  • completely solvable Lie algebras
  • left-invariant Riemannian metrics
  • Ricci curvature