The authors derive explicit SO(4)-invariant nearly-parallel G2 3-forms on S^7 and Berger's space, and show a hypersurface consistency condition determines their constants.
Ziller: On the geometry of cohomogeneity one manifol ds with positive curvature
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Revisiting 3-Sasakian and $G_2$-structures
The authors derive explicit SO(4)-invariant nearly-parallel G2 3-forms on S^7 and Berger's space, and show a hypersurface consistency condition determines their constants.