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Cohomogeneity one solitons for the isometric flow of [Formula: see text] -structures

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We consider the existence of cohomogeneity one solitons for the isometric flow of G 2 -structures on the following classes of torsion-free G 2 -manifolds: the Euclidean R 7 with its standard G 2 -structure, metric cylinders over Calabi-Yau 3-folds, metric... ...