Adapted metrics and Webster curvature in Finslerian 2-dimensional geometry (Q295945)

In the current paper, the Webster scalar curvature is computed for the sphere bundle \( T_{1}S \) for a Finsler surface \( (S,F) \) subject to the Chern-Hamilton notion of adapted metrics. As an application, it is derived that in this setting \( (T_{1}S,g_{\mathrm{Sasaki}}) \) is a Sasakian manifold homothetic to 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 \( T_{1}S \) is generally adapted to the natural co-frame provided by the Finsler structure.