Abstract.
We use a variational approach to prove that any nilpotent Lie algebra having a codimension-one abelian ideal, and anyone of dimension \(\leq 5\), admits a rank-one solvable extension which can be endowed with an Einstein left-invariant riemannian metric. A curve of \(8\)-dimensional Einstein solvmanifolds is also given.
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Received: 29 May 2001; in final form: 4 October 2001 / Published online: 4 April 2002
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Lauret, J. Finding Einstein solvmanifolds by a variational method. Math. Z. 241, 83–99 (2002). https://doi.org/10.1007/s002090100407
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DOI: https://doi.org/10.1007/s002090100407