The smoothness of Riemannian submersions with nonnegative sectional curvature

Jianguo Cao, Mei-Chi Shaw

Published 2003-09-19, updated 2003-09-26Version 2

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 $\Psi: M^n \to \Cal S$ must give rise to a $C^\infty$-smooth Riemannian submersion.