6533b7d6fe1ef96bd1265d42

RESEARCH PRODUCT

Homogeneous Weyl connections of non-positive curvature

Gabriela TereszkiewiczMaciej P. Wojtkowski

subject

Mathematics - Differential GeometryPure mathematics01 natural sciencesGaussian thermostatssymbols.namesake0103 physical sciencesFOS: MathematicsNon-positive curvatureNon-positive curvature0101 mathematicsConnection (algebraic framework)53C24 53C21Mathematics010102 general mathematicsMathematical analysisLie groupWeyl connectionsCartesian productManifoldUnimodular matrixDifferential Geometry (math.DG)Differential geometrysymbolsWeyl transformationMathematics::Differential Geometry010307 mathematical physicsGeometry and TopologyAnalysis

description

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.

https://doi.org/10.1007/s10455-016-9526-0