2010/03/09 by Jesse Alt, Alt, Jesse · 1 citation
Mathematics · #53C05 #53C15 #53C17 #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Holomorphic and Operator Theory #math.DG #msc:53C05 #msc:53C15 #msc:53C17
paper · pdf · doi:10.48550/arxiv.1003.1850
17 pages; references corrected, acknowledgement added
openalex publication_date 2010/03/09 · arxiv created 2010/03/16 · arxiv updated 2010/03/17 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We apply the theory of Weyl structures for parabolic geometries developed by A. Cap and J. Slovak in to compute, for a quaternionic contact (qc) structure, the Weyl connection associated to a choice of scale, i.e. to a choice of Carnot-Carathéodory metric in the conformal class. The result of this computation has applications to the study of the conformal Fefferman space of a qc manifold. In addition to this application, we are also able to easily compute a tensorial formula for the qc analog of the Weyl curvature tensor in conformal geometry and the Chern-Moser tensor in CR geometry. This tensor agrees with the formula derived via independent methods by S. Ivanov and D. Vasillev. However, as a result of our derivation of this tensor, its fundamental properties -- conformal covariance, and that its vanishing is a sharp obstruction to local flatness of the qc structure -- follow as easy corollaries from the general parabolic theory.