Flats and Submersions in Non-Negative Curvature

Curtis Pro, Frederick Wilhelm

Published 2011-04-27, updated 2012-01-03Version 3

We find constraints on the extent to which O'Neill's horizontal curvature equation can be used to create positive curvature on the base space of a Riemannian submersion. In particular, we study when K. Tapp's theorem on Riemannian submersions of compact Lie groups with bi-invariant metrics generalizes to arbitrary manifolds of non-negative curvature.