Prescribed Ricci tensor in Finslerian conformal class

Abstract

In this paper, a new geometric quantity, the trace-free horizon- tal Ricci tensor of a Finsler manifold is proposed. The conformal changes of this tensor, relatively to the conformal deformations of Finsler metrics when an Ehresmann form varies, are studied. As an application, it is shown that on a closed manifold two conformal Finsler metrics with the same horizontal Ricci tensor must be homothetic.