On Flag Curvature and Homogeneous Geodesics of Left Invariant Randers Metrics on the Semi-Direct Product a ⊕p r

We study flag curvature and homogeneous geodesics of left invariant Randers metrics on the Lie group with Lie algebra a p r, where a and r are abelian Lie algebra of dimension n and 1 , respectively.We give their flag curvature formulas explicitly.We show that there is an (n + 1)-dimensional Lie group with left invariant Randers metric which admits exactly one homogeneous geodesic.