Convex Projective Surfaces with Compatible Weyl Connection are Hyperbolic

Thomas Mettler

Institut für Mathematik, Goethe-Universität Frankfurt, Frankfurt am Main, Germany

Gabriel P. Paternain

Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, England

Date: 27th February 2019

Published Version: Anal. PDE 13 (2020), 1073—1097

1 Introduction
2 Preliminaries
2.1 The frame bundle
2.2 Conformal connections
2.3 The unit tangent bundle
2.4 Weyl connections
3 Projective thermostats
3.1 A characterisation of projective thermostats
3.2 The effect of a conformal change
4 Holomorphic curves
4.1 A complex surface
4.2 Möbius action
4.3 The Beltrami differential
5 The transport equation
6 The tensor tomography result
Appendix A Deriving the transport equation
References