Deformations of the Veronese Embedding and Finsler 2-Spheres of Constant Curvature

Christian Lange

Christian Lange, Mathematisches Institut der Universität München, Theresienstr. 39, D-80333 Munich, Germany

Thomas Mettler

Thomas Mettler, Institut für Mathematik, Goethe-Universität Frankfurt, Robert-Mayer-Str. 10, D-60325 Frankfurt am Main, Germany

Date: 13th March 2021

1 Introduction
1.1 Background
1.2 A duality result
1.3 Construction of examples
2 Preliminaries
2.1 Background on orbifolds
2.2 Besse orbifolds
2.3 Finsler structures.
2.4 Weyl structures and connections
3 A Duality Theorem
4 Construction of Examples
4.1 The twistor space
4.2 The Fubini--Study metric on the weighted projective line
4.3 Constructing the twistor space
4.4 Embedding the twistor space
4.5 Projective transformations
4.6 Deformations of Finsler metrics and the Veronese embedding
Appendix A The Biholomorphism for the \(2\)-Sphere
References