2014/04/14 by Xiaoyang Chen, Karsten Grove, Chen, Xiaoyang +1 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1404.3777
openalex publication_date 2014/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive general structure and rigidity theorems for submetries f: M → X, where M is a Riemannian manifold with sectional curvature \sec M ≥ 1. When applied to a non-trivial Riemannian submersion, it follows that diam X ≤ π/2 . In case of equality, there is a Riemannian submersion \mathbbS → M from a unit sphere, and as a consequence, f is known up to metric congruence. A similar rigidity theorem also holds in the general context of Riemannian foliations.