Some Special Metrics Of Finsler Geometry

This article is composed of four chapters. The first chapter is introduction, in which we mainly introduce the overview of Finsler geometry and dynamic research as well as knowledges of Finsler geometry and some special Finsler metrics.In the second chapter, we give some basic knowledges in Finsler geometry.In the third chapter, we study a class of Finsler metrics composed by two Riemannian met-rics and a 1-form. We first give the equivalent conditions of those metrics which are projectively flat. Then we give the classification when those metrics are projectively flat and with constant flag curvature.The fourth chapter is based on the third chapter. We study the projective quality of a class of Finsler metrics which are composed of m Riemannian metrics and a 1-form. Further, we prove that projectively flat Finsler metrics with constant flag curvature in this class are local Minkowski.