The smoothness of Riemannian submersions with nonnegative sectional curvature

Jianguo Cao; Mei-Chi Shaw

The smoothness of Riemannian submersions with nonnegative sectional curvature

Differential Geometry 2007-05-23 v2

Authors: Jianguo Cao , Mei-Chi Shaw

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

Keywords

riemannian submersion nonnegative sectional curvature soul distance non-increasing retraction smooth manifold

Cite

@article{arxiv.math/0309328,
  title  = {The smoothness of Riemannian submersions with nonnegative sectional curvature},
  author = {Jianguo Cao and Mei-Chi Shaw},
  journal= {arXiv preprint arXiv:math/0309328},
  year   = {2007}
}

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