Metrisability of three-dimensional projective structures
arXiv:1712.06191
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 (4)
- A solution of a problem of Sophus Lie: Normal forms of 2-dim metrics admitting two projective vector fields
- Invariant characterization of Liouville metrics and polynomial integrals
- Four--Dimensional Metrics Conformal to Kahler
- Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction
Cited by in corpus (13)
- Open problems and questions about geodesics
- Four--Dimensional Metrics Conformal to Kahler
- Projective Compactifications and Einstein metrics
- Projective vs metric structures
- Self-Dual Conformal Gravity
- Finsler surfaces with prescribed geodesics
- Degree of mobility for metrics of lorentzian signature and parallel (0,2)-tensor fields on cone manifolds
- Differential invariants for cubic integrals of geodesic flows on surfaces
- Is dark energy meaningless?
- Fubini Theorem for pseudo-Riemannian metrics
- Metrisability of projective surfaces and pseudo-holomorphic curves
- Two-dimensional metrics admitting precisely one projective vector field
- On the geometry of conformal geodesics equations