2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65246We address the question: how large is the family of complete metrics with nonnegative sectional curvature on S^2xR^3? We classify the connection metrics, and give several examples of non-connection metrics. We provide evidence that the family is small by proving some rigidity results for metrics more general than connection metrics.Differential Geometry53C20text