The rigidity of conformal circle-preserving transformations on Berwaldian manifolds

We prove that a complete Berwaldian manifold $(M,F)$ admitting a nontrivial conformal circle preserving transformation (\cpt for short) must be Riemannian, provided that it has a dense subset on which no flag curvature vanishes (in particular, if $(M,F)$ has positive or negative flag curvature).