Homogeneous Weyl connections of non-positive curvature

Abstract

We study homogenous Weyl connections with non-positive sectional curvatures. The Cartesian product ${\mathbb{S}}^1\times M$ 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.

24 pages