On the geometry of randers manifolds

Randers manifolds are studied in the framework of the pullback bundle formalism, with the aid of intrinsic methods only. After checking a sufficient condition for a Randers manifold to be a Finsler manifold, we provide a systematic description of the Riemann-Finsler metric, the canonical spray, the Barthel endomorphism, the Berwald connection, the Cartan tensors and the Cartan vector field in this new setting. Finally, as an application of the new tools and geometric ideas developed here, we present an intrinsic proof of the celebrated theorem about a criterion for a Randers manifold to become a Berwald manifold.