Canonical connections of Finsler metrics and Finslerian connections on Riemannian metrics (Q1915099)

A procedure of associating a canonical connection to a given Finsler metric is described; the connections which are compatible with the metric are compared both to this connection and to the corresponding Cartan connection. A necessary and sufficient condition for a Finsler connection to be compatible with a Riemannian metric is given. Implications of the obtained results for the construction of Finslerian relativities and of Finslerian physical theories containing a Riemannian gravitational sector are also provided.