Adapted metrics and Webster curvature in Finslerian 2-dimensional geometry

The Webster scalar curvature is computed for the sphere bundle T1S of a Finsler surface (S, F) subject to the Chern-Hamilton notion of adapted metrics. As an application, it is derived that in this setting (T1S, gSasaki) is a Sasakian manifold homothetic with a generalized Berger sphere, and that a natural Cartan structure is arising from the horizontal 1-forms and the author associates a non-Einstein pseudo-Hermitian structure. Also, one studies when the Sasaki type metric of T1S is generally adapted to the natural co-frame provided by the Finsler structure.