Twisted submersions in nonnegative sectional curvature

2012/12/11 by Pablo Angulo Ardoy, Luis Guijarro, Angulo-Ardoy, Pablo +3 · 1 citation
Mathematics · Physics and Astronomy · #53C20 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1212.2569

openalex publication_date 2012/12/11 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

B. Wilking introduced the dual foliation associated to a metric foliation in a Riemannian manifold with nonnegative sectional curvature, and proved that when the curvature is strictly positive, the dual foliation contains a single leaf, so that any two points in the ambient space can be joined by a horizontal curve. We show that the same phenomenon often occurs for nonnegatively curved Riemannian submersions even without the strict positive curvature condition, and irrespective of the particular metric.

Cited by

• The dual foliation of polar actions on nonnegatively curved manifolds

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