Finsler conformal changes preserving the modified Ricci curvature

Abstract

On a Riemannian manifold, a Liouville transformation is a conformal change which preserves the Ricci tensor. In Finsler geometry, there are various types of Ricci curvature. By adding a Landsberg curvature term to the classical Ricci curvature, we consider the conformal transformations on a Finsler manifold such that this modified Ricci curvature is preserved. We prove that such conformal transformations are homothetic if the space is C-convex. The conformal rigidity for Landsberg surfaces is also obtained.