On the generalization of theorems from Riemannian to Finsler Geometry I: Metric Theorems

摘要

A method to generalize results from Riemannian Geometry to Finsler geometryis presented. We use the method to generalize several results that involve onlymetric conditions. Between them we show that the topology induced by theFinsler structure is equivalent to the manifold topology, we provide a newproof of the Hopf-Rinow theorem in Finsler geometry and we prove the existenceof the center of mass of a convex body when the non-symmetric distance functioncomes from a non-reversible Finsler function.