  One way of producing explicit Riemannian 6-manifolds with holonomy SU(3) is
by integrating a flow of SU(2)-structures on a 5-manifold, called the hypo
evolution flow. In this paper we classify invariant hypo SU(2)-structures on
nilpotent 5-dimensional Lie groups. We characterize the hypo evolution flow in
terms of gauge transformations, and study the flow induced on the variety of
frames on a Lie algebra taken up to automorphisms. We classify the orbits of
this flow for all hypo nilpotent structures, obtaining several families of
cohomogeneity one metrics with holonomy contained in SU(3). We prove that these
metrics cannot be extended to a complete metric, unless they are flat.
