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Adopting the pullback approach to global Finsler geometry, the aim of thepresent paper is to provide intrinsic (coordinate-free) proofs of the existenceand uniqueness theorems for the Chern (Rund) and Hashiguchi connections on aFinsler manifold. To accomplish this, we introduce and investigate the notionsof semispray and nonlinear connection associated with a given regularconnection, in the pullback bundle. Moreover, it is shown that for the theChern (Rund) and Hashiguchi connections, the associated semispray coincideswith the canonical spray and the associated nonlinear connection coincides withthe Barthel connection. Explicit intrinsic expressions relating theseconnections and the Cartan connection are deduced. Although our investigationis entirely global, the local expressions of the obtained results, whencalculated, coincide with the existing classical local results. We provide, forthe sake of completeness and for comparison reasons, two appendices, one ofthem presenting a global survey of canonical linear connections in Finslergeometry and the other presenting a local survey of our global approach.

A Global Approach to the Theory of Connections in Finsler Geometry