Geometric Theory of Weyl Structures

Andreas Cap

Faculty of Mathematics, University of Vienna, Oskar--Morgenstern--Platz 1, 1090 Wien, Austria

Thomas Mettler

Faculty of Mathematics, UniDistance Suisse, Schinerstrasse 18, 3900 Brig, Switzerland

Date: February 2, 2022

1 Introduction
2 The bundle of Weyl structures
2.1 Parabolic geometries
2.2 Weyl structures
2.3 The basic geometric structures on \(A\)
2.4 Relations between natural vector bundles
2.5 The Weyl connections
2.6 The universal Rho-tensor
2.7 Curvature and torsion quantities
3 The natural almost bi-Lagrangian structure
3.1 The almost bi-Lagrangian structure and torsion freeness
3.2 Local frames
3.3 The canonical metric
3.4 Geometry of Weyl structures
4 Relations to non-linear invariant PDE
4.1 A tractorial description of \(A\)
4.2 The projective Monge-Ampère equation
4.3 Interpretation in terms of Weyl structures
4.4 Invariant non-linear PDE for other AHS structures
References