Flats and Submersions in Non-Negative Curvature

Abstract

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.

10 pages

References in corpus (2)

• An exotic sphere with positive sectional curvature
• On one family of 13-dimensional closed Riemannian positively curved manifolds