  We study nonnegatively curved metrics on S^2xR^4. First, we prove rigidity
theorems for connection metrics; for example, the holonomy group of the normal
bundle of the soul must lie in a maximal torus of SO(4). Next, we prove that
Wilking's almost-positively curved metric on S2xS3 extends to a nonnegatively
curved metric on S^2xR^4 (so that Wilking's space becomes the distance sphere
of radius 1 about the soul). We describe in detail the geometry of this
extended metric.
