Riemannian Submersions Need Not Preserve Positive Ricci Curvature

2012/06/17 by Curtis Pro, Pro, Curtis, Frederick Wilhelm +1 · 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.1206.3766

openalex publication_date 2012/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If π:M→ B is a Riemannian Submersion and M has positive sectional curvature, O'Neill's Horizontal Curvature Equation shows that B must also have positive curvature. We show there are Riemannian submersions from compact manifolds with positive Ricci curvature to manifolds that have small neighborhoods of (arbitrarily) negative Ricci curvature, but that there are no Riemannian submersions from manifolds with positive Ricci curvature to manifolds with nonpositive Ricci curvature.

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• Do Riemannian Submersions Preserve Positive Intermediate Ricci Curvature?

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