Manifolds with an SU(2)-action on the tangent bundle

Roger Bielawski

Published 2003-09-18, updated 2003-09-23Version 2

We study manifolds arising as spaces of sections of complex manifolds fibering over the projective line with normal bundle of each section isomorphic to several copies of O(k). Such manifolds provide a natural setting for certain integrable systems, "monopoles", which comprise the Bogomolny hierarchy and the self-dual hierarchy.