A Class of Finsler Metrics with Constant Flag Curvature

Abstract

The local structure of Finsler metrics of constant flag curvature has been historically mysterious. In this paper, we obtain the class of metric is to be Einstein with constant Killing 1-form and also we obtained the necessary conditions that metric have constant flag curvature on a manifold of dimension. Then, we proved that such metric is either Riemannian or locally Minkowskian. Further, we gave the alternate proof as mention above result on the basis of elementary linear algebra.