ON THE CONSTRUCTION OF RIEMANNIAN METRICS FOR BERWALD SPACES BY AVERAGING

摘要

The construction of Riemannian metrics on the base manifold of any given Finsler space by averaging suitable objects over indicatrices, such that the Levi-Civita connection of the metric coincides with the canonical Berwald connection of the Finsler space when the Finsler space is a Berwald space, is discussed. Some examples of such metrics are already known, but several new ones, all in principle different, are defined and analysed.