Closed ${\mathrm{G}}_2$-structures with ${\mathbb{T}}^3$-symmetry and hypersymplectic structures

Chengjian Yao, Ziyi Zhou

We decompose linear ${\mathrm{G}}_2$-structure in canonical ways adapted to 3-dimensional subspaces, in terms of certain natural 1-forms and definite triple of 2-forms, and apply the…