Metrisability of three-dimensional projective structures

Abstract

We solve the metrisability problem for generic three-dimensional projective structures.

14 pages. As pointed out by Maciej Dunajski, the previous proof of Theorem 3 was incomplete. In this version, the proof is complete. Also, following helpful discussions with Felipe Contatto and Maciej Dunajski, Theorem 4 has been added

References in corpus (1)

• Invariant characterization of Liouville metrics and polynomial integrals

Cited by in corpus (4)

• Finsler surfaces with prescribed geodesics
• Is dark energy meaningless?
• Two-dimensional metrics admitting precisely one projective vector field
• On the geometry of conformal geodesics equations