Left Invariant Lifted (α, β)-metrics of Douglas Type on Tangent Lie Groups

In this paper we study lifted left invariant $(\alpha,\beta)$-metrics of Douglas type on tangent Lie groups. Let $G$ be a group equipped with $(\alpha,\beta)$-metric $F$, induced by Riemannian metric $g$. Using vertical and complete lifts, construct the $F^v$ $F^c$ $TG$ give necessary sufficient conditions for them to type. Then, flag curvature these metrics are studied. Finally, as some special cases, curvatures in cases Randers type, Kropina Matsumoto Berwald given.