Deformation quantization of almost Kähler models and Lagrange-Finsler spaces

Finsler and Lagrange spaces can be equivalently represented as almost Kähler manifolds endowed with a metric compatible canonical distinguished connection structure generalizing the Levi-Civita connection. The goal of this paper is to perform a natural Fedosov-type deformation quantization of such geometries. All constructions are canonically derived for regular Lagrangians and/or fundamental Finsler functions on tangent bundles.