2007/10/11 by Andreas Čap, Andreas Cap, Katja Sagerschnig · 3 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Differential Geometry Research #Class (philosophy) #Combinatorics #Conformal field theory #Conformal geometry #Conformal map #Connection (principal bundle) #Dimension (graph theory) #Distribution (mathematics) #Extremal length #Geometric Analysis and Curvature Flows #Geometry #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Metric (unit) #Primary field #Pure mathematics #Rank (graph theory) #Signature (topology) #Weyl transformation #math.DG #msc:53A30 #msc:53A40 #msc:53B15 #msc:53C50
paper · pdf · doi:10.1016/j.geomphys.2009.04.001
published as J. Geom. Phys. 59 (2009) 901-912 · AMSLaTeX, 23 pages
arxiv created 2007/10/11 · openalex publication_date 2009/04/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
For a generic distribution of rank two on a manifold M of dimension five, we introduce the notion of a generalized contact form. To such a form we associate a generalized Reeb field and a partial connection. From these data, we explicitly constructed a pseudo--Riemannian metric on M of split signature. We prove that a change of the generalized contact form only leads to a conformal rescaling of this metric, so the corresponding conformal class is intrinsic to the distribution. In the second part of the article, we relate this conformal class to the canonical Cartan connection associated to the distribution. This is used to prove that it coincides with the conformal class constructed by Nurowski.