Flats in Riemannian Submersions from Lie Groups

TL;DR

This paper proves that in Riemannian submersions from compact Lie groups with bi-invariant metrics, the base space exhibits a property where zero-curvature planes exponentiate to flats, extending known results for normal biquotients.

Contribution

It establishes a new geometric property of base spaces in Riemannian submersions from compact Lie groups, generalizing previous results for biquotients.

Findings

Zero-curvature planes exponentiate to flats in the base space.

The property holds for Riemannian submersions from compact Lie groups with bi-invariant metrics.

Extends known results from normal biquotients to a broader class of submersions.

Abstract

We prove that any base space of Riemannian submersion from a compact Lie group (with bi-invariant metric) must have a basic property previously known for normal biquotients; namely, any zero-curvature plane exponentiates to a flat.