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Siberian Advances in Mathematics

, Volume 24, Issue 1, pp 18–25 | Cite as

The Ricci operator of completely solvable metric lie algebras

  • M. S. Chebarykov
  • Yu. G. Nikonorov
Article
  • 44 Downloads

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.

Keywords

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

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Copyright information

© Allerton Press, Inc. 2014

Authors and Affiliations

  1. 1.Rubtsovsk Industrial InstituteRubtsovskRussia
  2. 2.Southern Mathematical Institute of the Vladikavkaz Scientific Center of the RASVladikavkazRussia

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