  of the equivalence class \(K\) of conformally equivalent symmetric linear connections, and the equivalence class \(\Pi\) of projectively  equivalent symmetric linear connections, contains a unique symmetric  linear connection, a Weyl connection. Thus light propagation and free (fall) motion reveal on spacetime a unique Weyl connection  which determines the parallel transport of vectors, preserving their  timelike, null or spacelike character, and for any pair of non-null  vectors, the Weyl connection leaves invariant the ratio of their  lengths and the angle between them, provided the vectors are  transported along the same path. 