Closed G2-structures with T3 symmetry reduce to hypersymplectic or flat/hyperkahler structures under completeness and constant volume assumptions.
Differential Geom.111(2019), no
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Closed $\mathrm{G}_2$-structures with $\mathbb{T}^3$-symmetry and hypersymplectic structures
Closed G2-structures with T3 symmetry reduce to hypersymplectic or flat/hyperkahler structures under completeness and constant volume assumptions.