Annals of Global Analysis and Geometry

, Volume 33, Issue 1, pp 71–87 | Cite as

Einstein solvmanifolds with free nilradical

  • Yuri NikolayevskyEmail author
Original Paper


We classify solvable Lie groups with a free nilradical admitting an Einstein left-invariant metric. Any such group is essentially determined by the nilradical of its Lie algebra, which is then called an Einstein nilradical. We show that among the free Lie algebras, there are very few Einstein nilradicals. Except for the Abelian and the two-step ones, there are only six others: \({\mathfrak{f}}(2,3), {\mathfrak{f}}(2,4), {\mathfrak{f}}(2,5), {\mathfrak{f}}(3,3), {\mathfrak{f}}(4,3), {\mathfrak{f}}(5,3) (here {\mathfrak{f}}(m,p)\) is a free p-step Lie algebra on m generators). The reason for that is the inequality-type restrictions on the eigenvalue type of an Einstein nilradical obtained in the paper.


Einstein nilradical Free Lie algebra 

Mathematics Subject Classification (2000)

53C30 53C25 


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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of MathematicsLa Trobe UniversityMelbourneAustralia

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