Exact G${}_2$-structures on compact quotients of Lie groups

Abstract

We show that the compact quotient $\Gamma \backslash \mathrm{G}$ of a seven-dimensional simply connected Lie group $\mathrm{G}$ by a co-compact discrete subgroup $\Gamma \subset \mathrm{G}$ does not admit any exact ${\mathrm{G}}_2$-structure which is induced by a left-invariant one on $\mathrm{G}$.

25 pages. v2: revised version. To appear in Annali di Matematica Pura ed Applicata

References in corpus (2)

• A new example of a compact ERP G2-structure
• Exact $G_2$-structures on unimodular Lie algebras