Ricci flow of warped Berger metrics on {mathbb {R}}^{4}

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We study the Ricci flow on {mathbb {R}}^{4} starting at an SU(2)-cohomogeneity 1 metric g_{0} whose restriction to any hypersphere is a Berger metric. We prove that if g_{0} has no necks and is bounded by a cylinder, then the solution develops a global Type-II singularity and converges to the Bryant soliton when suitably dilated at the origin. This is the first example in dimension n > 3 of a non-rotationally symmetric Type-II flow converging to a rotationally symmetric singularity model. Next, we show that if instead g_{0} has no necks, its curvature decays and the Hopf fibres are not collapsed, then the solution is immortal. Finally, we prove that if the flow is Type-I, then there exist minimal 3-spheres for times close to the maximal time.