  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.
