Flats in Riemannian Submersions from Lie Groups

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.

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• An exotic sphere with positive sectional curvature
• Some Principles for Deforming Nonnegative Curvature