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arXiv · 1908.05975

Diagram involutions and homogeneous Ricci-flat metrics

Diego Conti·Viviana del Barco·Federico A. Rossi
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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 ${\rm SL}(n)$, ${\rm SO}(p,q)$, ${\rm Sp}(n,\mathbb R)$. Most of these metrics are shown not to be flat.

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Diego Conti, Viviana del Barco, Federico A. Rossi. 2019-08-16. Diagram involutions and homogeneous Ricci-flat metrics. https://doi.org/10.1007/s00229-020-01225-y

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