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

A criterion for compatibility of conformal and projective structures