In this paper, we employ two geometries as Riemannian and Finsler geometry. In that case, we take two metrics background as FRW and Godel metrics. They play important roles in explanation of several phenomena in cosmology. And then, we calculate the Killing vec- tors that correspond with two metrics by using two geometries. Also, we obtain the generators of algebra and compare two geometries from Killing vector point of view. Finally, we achieve the commutation relations of such geometries from two metrics background.
