The smoothness of Riemannian submersions with nonnegative sectional curvature

Details The smoothness of Riemannian submersions with nonnegative sectional curvature The smoothness of Riemannian submersions with nonnegative sectional curvature

2003-09-19

arxiv.org/abs/math/0309328v2

Mathematics

Differential Geometry

Scientific paper

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.

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