Finslerian Ricci Deformation and Conformal Metrics

Abstract

In this paper, a new Ricci flow is canonically introduced in Finsler Geometry and, under the variance of Finsler-Ehresmann form, conformal changes of Finsler metrics are studied. Some existence conditions of this Finslerian Ricci flow on a compact manifold which preserves the conformal class of the initial metric are obtained as an application.