On classification of Finslerian spaces with nontrivial concircular transformations

Abstract

We prove that in a non-trivial conformal circle-preserving transformation (CPT for short), $e^σF$ on a (forward or backward) complete Finslerian manifold $(M,F)$, the conformal factor has at most two critical points. Then a diffeomorphism classification based on the number of critical points as well as some curvature rigidity properties - of Finslerian manifolds that admit nontrivial conformal CPTs - is presented.