This article is cited in 2 papers

The Ricci operator of completely solvable metric Lie algebras

Yu. G. Nikonorov^a, M. S. Chebarykov<sup>b

a</sup> 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.

UDC: 514.765

Received: 07.11.2011

 English version: Siberian Advances in Mathematics, 2014, 24:1, 18–25

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