Seminarium Teorii Względności i Grawitacji

In a space-time M, a conformal structure C is defined by the distribution of light-cones. Geodesics are traced by freely falling particles and the collection of all unparametrized geodesics determines the projective structure P of M. In the talk, there will be given a short history of the problem of compatibility between C and P. Necessary and sufficient conditions for C and P to be compatible, found recently by Vladimir Matveev, are expressed by simple tensorial equations that allow an explicit determination of the metric tensor underlying these structures.