Generalized Fermi transport in generalized gravitation theories

If geodesics in space-time can be classified as timelike, null, and spacelike, the affine connection must be of the form Γ_jk ⁱ = {_jkⁱ}+2g^iae_jka- (δ_jⁱδ_k^a+δ _kⁱδ_j^a-g _jkg ^ia)d _a, with d _a, an arbitrary vector and e _ijk a tensor satisfying e_(ijk)=e_[ij]k=0. It is possible to generalize Fermi's law of transport to this affine connection. The requirement that any observer be able to construct and maintain a nonrotating orthogonal space triad along his world line by the bouncing photon experiment implies the Weyl's geometry of paths.