Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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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

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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