Generalized Finsler geometry and its Cartan connection in modification   of special relativity
  The generalized Finsler geometry, as well as Finsler geometry, is a generalization of Riemann geometry. The generalized Finsler geometry can be endowed with the Cartan connection. The generalized Finsler geometry and its Cartan connection are, as the necessary mathematical tools, involved in our modification of special relativity, which is made by assuming the generalized Finslerian structures of gravity-free space and time in the usual inertial coordinate system and combining this assumption with two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the speed of light in all inertial frames of reference. 
Jian-Miin Liu