Geodesic
The Ricci operator of completely solvable metric Lie algebras
Matematičeskie trudy, Tome 15 (2012) no. 2, pp. 146-158

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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. 
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     author = {Yu. G. Nikonorov and M. S. Chebarykov},
     title = {The {Ricci} operator of completely  solvable metric {Lie} algebras},
     journal = {Matemati\v{c}eskie trudy},
     pages = {146--158},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2012_15_2_a8/}
}
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Yu. G. Nikonorov; M. S. Chebarykov. The Ricci operator of completely  solvable metric Lie algebras. Matematičeskie trudy, Tome 15 (2012) no. 2, pp. 146-158. http://geodesic.mathdoc.fr/item/MT_2012_15_2_a8/