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Geometriae Dedicata

, Volume 170, Issue 1, pp 119–133 | Cite as

Negative eigenvalues of the Ricci operator of solvable metric Lie algebras

  • Yu. G. Nikonorov
Article

Abstract

In this paper we get a necessary and sufficient condition for the Ricci operator of a solvable metric Lie algebra to have at least two negative eigenvalues. In particular, this condition implies that the Ricci operator of every non-unimodular solvable metric Lie algebra or every non-abelian nilpotent metric Lie algebra has this property.

Keywords

Left-invariant Riemannian metrics Lie groups Metric Lie algebras  Ricci operator Eigenvalues of the Ricci operator Ricci curvature 

Mathematical Subject Classification (2010)

53C30 17B30 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.South Mathematical Institute of Vladikavkaz Scientific Centre of the Russian Academy of SciencesVladikavkazRussia

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