Geodesic vectors of (α, β)-metrics on hypercomplex 4-dimensional Lie groups

In this paper, we consider invariant (α, β)-metrics and describe all geodesic vectors and investigate the set of all homogeneous geodesics on left invariant hypercomplex four dimensional simply connected Lie groups. Also, we study the conditions for the Douglas and Berwald type of (α, β)-metrics on the left invariant hypercomplex four dimensional simply connected Lie groups.