2012/07/17 by Marc Herzlich, Herzlich, Marc
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #math.DG
paper · pdf · doi:10.48550/arxiv.1207.4005
arxiv created 2012/07/17 · openalex publication_date 2012/07/17 · arxiv updated 2012/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a simple characterization of the parabolic geodesics introduced by Cap, Slovak and Zadnik for all parabolic geometries. This goes through the definition of a natural connection on the space of Weyl structures. We then show that parabolic geodesics can be characterized as the following data: a curve on the manifold and a Weyl structure along the curve, so that the curve is a geodesic for its companion Weyl structure and the Weyl structure is parallel along the curve and in the direction of the tangent vector of the curve.