Closed ${\mathrm{G}}_2$-eigenforms and exact ${\mathrm{G}}_2$-structures

Marco Freibert, Simon Salamon

A study is made of left-invariant ${\mathrm{G}}_2$-structures with an exact 3-form on a Lie group $G$ whose Lie algebra $\mathfrak{g}$ admits a codimension-one nilpotent ideal $\math…