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The smoothness of Riemannian submersions with nonnegative sectional curvature

Jianguo Cao·Mei-Chi Shaw
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Abstract

Let $M^n$ be a complete, non-compact and $C^\infty$-smooth Riemannian manifold with nonnegative sectional curvature. Suppose $\Cal S$ is a soul of $M^n$. Then any distance non-increasing retraction $Ψ: M^n \to \Cal S$ must give rise to a $C^\infty$-smooth Riemannian submersion.

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Jianguo Cao, Mei-Chi Shaw. 2003-09-26. The smoothness of Riemannian submersions with nonnegative sectional curvature. https://arxiv.org/abs/math/0309328

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