Finslerian complex and Kählerian structures

In this article, we study a class of gg-natural metrics on the tangent bundle of a Finsler manifold which is a generalized version of Sasaki–Matsumoto metric and Miron metric. Then, we consider on compatible almost complex structure with together the metric confers to the slit tangent bundle of Finsler manifold and structure of locally conformal almost Kählerian manifold. We find some conditions under which the slit tangent bundle is locally conformal Kählerian, Kählerian, locally Euclidean or the Finsler manifold has scalar or constant flag curvature.