Study of geodesic equations of Randers metrics on para-hypercomplex Lie groups

In this paper, we study the ۴-dimensional para-hypercomplex Lie groups equipped with a left invariant Randers metric. We first get all the equations related to geodesic vectors on four dimensional para-hypercomplex Lie groups. Finally, we show the condition of the equivalence of geodesic vectors in the Riemannian and Finslerian spaces.

کلیدواژه ها:

Geodesic equation ، geodesic vector ، Lie groups ، Para-hypercomplex structure ، Randers metric