We introduce a combinatorial method to construct indefinite Ricci-flat metrics on nice nilpotent Lie groups. We prove that every nilpotent Lie group of dimension $leq6$, every nice nilpotent Lie group of dimension $leq7$ and every two-step nilpotent Lie group attached to a graph admits such a metric. We construct infinite families of Ricci-flat nilmanifolds associated to parabolic nilradicals in the simple Lie groups SL(n), SO(p,q), Sp(n,R). Most of these metrics are shown not to be flat.
Conti, D., del Barco, V., Rossi, F. (2021). Diagram involutions and homogeneous Ricci-flat metrics. MANUSCRIPTA MATHEMATICA, 165(3-4), 381-413 [10.1007/s00229-020-01225-y].
Diagram involutions and homogeneous Ricci-flat metrics
Conti, Diego;Rossi, Federico A.
2021
Abstract
We introduce a combinatorial method to construct indefinite Ricci-flat metrics on nice nilpotent Lie groups. We prove that every nilpotent Lie group of dimension $leq6$, every nice nilpotent Lie group of dimension $leq7$ and every two-step nilpotent Lie group attached to a graph admits such a metric. We construct infinite families of Ricci-flat nilmanifolds associated to parabolic nilradicals in the simple Lie groups SL(n), SO(p,q), Sp(n,R). Most of these metrics are shown not to be flat.
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