1302.2329 (Vladimir S. Matveev et al.)

A criterion for compatibility of conformal and projective structures    [PDF]

Vladimir S. Matveev, Andrzej Trautman

In a space-time, a conformal structure is defined by the distribution of light-cones. Geodesics are traced by freely falling particles, and the collection of all unparameterized geodesics determines the projective structure of the space-time. The article contains a formulation of the necessary and sufficient conditions for these structures to be compatible, i.e. to come from a metric tensor which is then unique up to a constant factor. The theorem applies to all dimensions and signatures.

View original: http://arxiv.org/abs/1302.2329