An intrinsic curvature condition for submersions over Riemannian manifolds

2017/06/28 by Llohann D. Sperança, Sperança, Llohann D.
Mathematics · Physics and Astronomy · #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.1706.09211

openalex publication_date 2017/06/28 · openalex created_date 2017/07/14 · openalex updated_date 2026/07/28

Abstract

Let π: (M,H)→ (B,b) be a submersion equipped with a horizontal connection \cal H over a Riemannian manifold (B,b). We present an intrinsic curvature condition that only depends on the pair (\cal H,b). By studying a set of relative flat planes, we prove that a certain class of pairs (\cal H,b) admits a compatible metric with positive sectional curvature only if they are fat, verifying Wilhelm's Conjecture in this class.

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