Adapted metrics and Webster curvature in Finslerian 2-dimensional geometry

Abstract

The Webster scalar curvature is computed for the sphere bundle T ₁ S 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 (T ₁ S, g _Sasaki) 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 T ₁ S is generally adapted to the natural co-frame provided by the Finsler structure.

Keywords

Webster curvature / Finsler geometry / Sasakian type metric on tangent bundle / Sphere bundle / Adapted metric / Cartan structure / Pseudo-Hermitian structure

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