Metrics with nonnegative curvature on \({S^2 \times \mathbb{R}^4}\) (Q420606)

This article is about Riemannian metrics of nonnegative sectional curvature on \(S^2\times \mathbb{R}^4\). The first result is a rigidity result for a special type of metrics called connection metrics. It is proved that for such metrics, the holonomy group of the normal bundle of the soul lies in a maximal torus of \(\mathrm{SO}(4)\). The article goes on to construct a metric on \(S^2\times \mathbb{R}^4\) which is an extension of a metric on \(S^2\times S^3\) constructed by Wilking, which has positive sectional curvature almost everywhere. Some properties of this extension are given.