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 ${\Gamma }_{\mathrm{jk}}^i{\mathrm{=\{}}_{\mathrm{jk}}^i{\text{}+2g}}^{\mathrm{ia}}{e}_{\mathrm{jka}}{\mathrm{-(\delta }}_j^i{\delta }_k^a{\mathrm{+\delta }}_k^i{\delta }_j^a{\mathrm{-g}}_{\mathrm{jk}}{g}^{\mathrm{ia}}{\mathrm{)d}}_a$ , 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.