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.
Diagram involutions and homogeneous Ricci-flat metrics
Conti, Diego;
2021-01-01
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.File in questo prodotto:
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