A NEW APPROACH TO GENERALIZED BERWALD MANIFOLDS II

Generalized Berwald manifolds were introduced by V. V. Wagner and systematically investigated by M. Hashiguchi and Y. Ichijyō. They are reconsidered here in the context and with the tools of the general theory developed in the first part of our work. (However, this second part is self-contained to a reasonable extent.) Under some natural conditions we establish key relations between a horizontal endomorphism and the distinguished Barthel endomorphism on a Finsler manifold. We construct intrinsically a vector field which plays a dominant role in these and further, geometrically relevant relations. In the case of a generalized Berwald man-ifold (M, E,∇) the linear connection ∇ is far from unique. Our results enable us to link different generalized Berwald manifolds with common Finsler structure. Applications to Wagner manifolds and a family of examples (parallelizable manifolds endowed with one-form Finsler structure) illustrate how the general theory works in practice