Weyl metrisability of two-dimensional projective structures

Thomas Mettler

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, United Kingdom

Date: May 22, 2013

Published Version: Math. Proc. Camb. Philos. Soc. 156 (2014), 99—113

1 Introduction
2 An EDS solution for local Weyl metrisability
2.1 Cartan's projective connection
2.2 Coordinate sections of Cartan's bundle
2.3 Coordinate sections and Weyl metrisability
3 A complex geometry solution for Weyl metrisability
3.1 The bundle of conformal inner products
3.2 The complex surface \(\mathcal{C}(M)\) and Cartan's connection
3.3 The compatibility problem and holomorphic curves
4 The flat case
4.1 Cartan's connection in the flat case
4.2 The bundle of conformal inner products in the flat case
4.3 Weyl connections on \(\mathbb{S}^2\) and smooth quadrics \(Q\subset \mathbb{CP}^2\)
References