## D. Conti - V. Del Barco - F. A. Rossi

# Diagram involutions and homogeneous Ricci-flat metrics

created by rossi on 03 Sep 2019

modified on 27 Apr 2022

[

BibTeX]

*Published Paper*

**Inserted:** 3 sep 2019

**Last Updated:** 27 apr 2022

**Journal:** Manuscripta Mathematica

**Volume:** 165.3-4

**Pages:** 381–413

**Year:** 2021

**Doi:** 10.1007/s00229-020-01225-y

**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.