Canonical corrections of Finsler metrics and Finslerian connections on Riemannian metrics

A concept of canonical connection of a Finsler metric is developed. Connections that are compatible with Finsler metrics are compared with the canonical connection itself. They are also compared with the corresponding Cartan connection. A necessary and sufficient condition on metric Finsler connections is given for the metric to be Riemannian. This study unearths different ways in which Finsler geometry could be used to generalize the theory of general relativity.