Rigidity for Nonnegatively Curved Metrics on S^2xR^3
  We 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. 
Kristopher Tapp