Cohomogeneity one solitons for the isometric flow of -structures.

We consider the existence of cohomogeneity one solitons for the isometric flow of -structures on the following classes of torsion-free -manifolds: the Euclidean with its standard -structure, metric cylinders over Calabi-Yau 3-folds, metric cones over nearly Kähler 6-manifolds, and the Bryant-Salamon -manifolds. In all cases we establish existence of global solutions to the isometric soliton equations, and determine the asymptotic behaviour of the torsion. In particular, existence of shrinking isometric solitons on is proved, giving support to the likely existence of type I singularities for the isometric flow.