A classification of complete Finsler manifolds through the conformal theory of curves

In the first part of this work we are going to touch the conformal theory of curves on Finsler geometry, emphasizing on the notion of circles preserving transformations, recently studied by the present author and Z. Shen. Next, the conformal changes of metrics which leave invariant geodesic circles known as concircular transformation are characterized by a second order differential equation. As an application a classification of complete Finsler manifolds admitting such transformations is obtained.