GENERALIZED BERWALD SPACES AS AFFINE DEFORMATIONS OF MINKOWSKI SPACES

Generalized Berwald spaces are the Finsler spaces which admit metric linear connections in the tangent bundle of their base manifold. They reduce to Berwald spaces if the torsion of this connection vanishes. We show that generalized Berwald spaces with base manifold R-n are exactly the affine deformations of Minkowski spaces. They can also be represented as a pair of a Riemannian and a Minkowski space, and they coincide with the Finsler spaces of 1-form metric. We investigate their reduction to Minkowski, Riemannian or Euclidean spaces, as well as their conformal relations.