We study a special class of Finsler metrics which we refer to as Almost Rational (shortly, AR-Finsler metrics). give necessary and sufficient conditions for an manifold (M, F) be Riemannian. The rationality some geometric objects such Cartan torsion, geodesic spray, Landsberg curvature S-curvature is investigated. For particular subfamily have proved that if F has isotropic S-curvature, then th...

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 specia...