REVERSIBLE GEODESICS FOR (α, β)-METRICS

A Finsler space is said to have reversible geodesics if for any of its oriented geodesic paths, the same path traversed in the opposite sense is also a geodesic. In [6] the conditions for a Randers space to have reversible geodesics have been found. The main goal of this paper is to find conditions for a Finsler space endowed with an (α, β)-metric to be with reversible geodesics or strictly reversible geodesics, respectively. Moreover, we obtain some new classes of (α, β)-metrics with reversible geodesics and show how new Finsler metrics with reversible geodesics can be constructed by means of a Randers change.