Diagram involutions and homogeneous Ricci-flat metrics

created by rossi on 03 Sep 2019

[BibTeX]

preprint

Inserted: 3 sep 2019
Last Updated: 3 sep 2019

Year: 2019

ArXiv: 1908.05975 PDF

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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