Holonomy Theory of Finsler Manifolds

Abstract

The holonomy group of a Riemannian or Finslerian manifold can be introduced in a very natural way: it is the group generated by parallel translations along loops with respect to the canonical connection. The Riemannian holonomy groups have been extensively studied and by now their complete classification is known. On the Finslerian holonomy, however, only few results are known and, as our results show, it can be essentially different from the Riemannian one.