Metrisability of three-dimensional path geometries
Differential Geometry seminars, 13th and 19th August 2014

Abstract Given a projective structure on a three-dimensional manifold, we find some explicit obstructions to the local existence of a Levi-Civita connection in the projective class (given as projectively invariant tensors algebraically constructed from the projective Weyl curvature). There will be examples. This is joint work with Maciej Dunajski.

Here is the arXiv article on which these talks were based.