Flats and Submersions in Non-Negative Curvature

TL;DR

This paper investigates the limitations of using O'Neill's horizontal curvature equation to induce positive curvature in the base space of Riemannian submersions, especially in the context of non-negative curvature manifolds.

Contribution

It analyzes the applicability of Tapp's theorem beyond compact Lie groups, extending understanding of curvature constraints in Riemannian submersions.

Findings

Identifies constraints on creating positive curvature via submersions

Determines when Tapp's theorem generalizes to non-Lie manifolds

Provides conditions for curvature behavior in non-negative curvature settings

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.