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 Γjki={jki}+2giaejka−(δjiδka+δkiδja−gjkgia)da, with da an arbitrary vector and eijk 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.