Homogeneous Weyl connections of non-positive curvature

2015/06/26 by Gabriela Tereszkiewicz, Maciej P. Wojtkowski, Tereszkiewicz, Gabriela +1
Mathematics · #53C21 #53C24 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1506.08176

openalex publication_date 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study homogenous Weyl connections with non-positive sectional curvatures. The Cartesian product \mathbb S¹ × M carries canonical families of Weyl connections with such a property, for any Riemmanian manifold M. We prove that if a homogenous Weyl connection on a manifold, modeled on a unimodular Lie group, is non-positive in a stronger sense (streched non-positive), then it must be locally of the product type.

Citations

• Curvatures of left invariant metrics on lie groups

Related

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• Non-negative curvature on certain product manifolds
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• A natural connection on a basic class of Riemannian product manifolds