Left invariant Randers metrics of Berwald type on tangent Lie groups

Let G be a Lie group equipped with a left invariant Randers metric of Berward type F, with underlying left invariant Riemannian metric g. Suppose that F and g are lifted Randers and Riemannian metrics arising from F and g on the tangent Lie group TG by vertical and complete lifts. In this paper, we study the relations between the flag curvature of the Randers manifold (TG,F) and the sectional curvature of the Riemannian manifold (G,g) when F is of Berwald type. Then we give all simply connected three-dimensional Lie groups such that their tangent bundles admit Randers metrics of Berwarld type and their geodesics vectors.