Every nilpotent Lie group of dimension at most 6, every nice nilpotent Lie group of dimension at most 7, and every two-step nilpotent Lie group associated to a graph admits an indefinite Ricci-flat metric, almost always nonflat.
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Diagram involutions and homogeneous Ricci-flat metrics
Every nilpotent Lie group of dimension at most 6, every nice nilpotent Lie group of dimension at most 7, and every two-step nilpotent Lie group associated to a graph admits an indefinite Ricci-flat metric, almost always nonflat.