  A geodesic circle in Finsler geometry is a natural extension of that in a
Euclidean space. In this paper, we apply Lie derivatives and the Cartan
$Y$-connection to study geodesic circles and (infinitesimal) concircular
transformations on a Finsler manifold. We characterize a concircular vector
field with some PDEs on the tangent bundle, and then we obtain respective
necessary and sufficient conditions for a concircular vector field to be
conformal and a conformal vector field to be concircular. We also show
conditions for two conformally related Finsler metrics to be concircular, and
obtain some invariant curvature properties under conformal and concircular
transformations.
