Papers › A construction of Einstein solvmanifolds not based on nilsolitons
A construction of Einstein solvmanifolds not based on nilsolitons
Diego Conti, Federico A. Rossi, Romeo Segnan Dalmasso
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We construct indefinite Einstein solvmanifolds that are standard, but not of pseudo-Iwasawa type. Thus, the underlying Lie algebras take the form 𝔤⋊_Dℝ, where 𝔤 is a nilpotent Lie algebra and D is a nonsymmetric derivation. Considering nonsymmetric derivations has the consequence that 𝔤 is not a nilsoliton, but satisfies a more general condition. Our construction is based on the notion of nondiagonal triple on a nice diagram. We present an algorithm to classify nondiagonal triples and the associated Einstein metrics. With the use of a computer, we obtain all solutions up to dimension 5, and all solutions in dimension ≤9 that satisfy an additional technical restriction. By comparing curvatures, we show that the Einstein solvmanifolds of dimension ≤5 that we obtain by our construction are not isometric to a standard extension of a nilsoliton.
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