Convergence of Ricci flow solutions to Taub-NUT

Abstract

We study the Ricci flow starting at an SU(2) cohomogeneity-1 metric g 0 on R 4 with monotone warping coefficients and whose restriction to any hypersphere is a Berger metric. If g 0 has bounded Hopf-fiber, curvature controlled by the size of the orbits and opens faster than a paraboloid in the directions orthogonal to the Hopf-fiber, then the flow converges to the Taub-NUT metric g TNUT in the Cheeger-Gromov sense in infinite time. We also classify the long-time behaviour when g 0 is asymptotically flat. In order to identify infinite-time singularity models we obtain a uniqueness result for g TNUT : ARTICLE HISTORY