A Global Approach to the Theory of Connections in Finsler Geometry

Understand

Adopting the pullback approach to global Finsler geometry, the aim of the present paper is to provide intrinsic (coordinate-free) proofs of the existence and uniqueness theorems for the Chern (Rund) and Hashiguchi connections on a Finsler manifold.

• To accomplish this, we introduce and investigate the notions of semispray and nonlinear connection associated with a given regular connection, in the pullback bundle.
• Moreover, it is shown that for the the Chern (Rund) and Hashiguchi connections, the associated semispray coincides with the canonical spray and the associated nonlinear connection coincides with the Barthel connection.
• Explicit intrinsic expressions relating these connections and the Cartan connection are deduced.