Nearly parallel G2-structures with 3-torus symmetry reduce to two triples of closed 2-forms on 3-manifolds related by a Riemannian metric, with an explicit inverse construction from the 3D data.
Complete hyper-K¨ ahler 4n-manifolds with a local tri-Hamiltonian Rn-action
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Nearly Parallel $\mathrm{G}_{2}$-Structures with Torus Symmetry
Nearly parallel G2-structures with 3-torus symmetry reduce to two triples of closed 2-forms on 3-manifolds related by a Riemannian metric, with an explicit inverse construction from the 3D data.