On Some Finsler Metrics With Special Projective Properties

This article divides into four chapters,the first chapter introduces the history of Finsler geometry and some basic knowledges.In the second chapter,we discuss a class of Finsler metrics F=(?)+C with double square roots,and give the classification of them under the condition of projectively flat and constant flag curvature.In the third chapter we discuss the solution of PDE fxk(x,y)=f(x,y)fyk(x,y) in the Finsler geometry,where fxk(x,y)=(?)f(x,y)/(?)xk and fxk(x,y)=(?)f(x,y)/(?)yk,Then get some of the relationship between the coefficients of them by using series expansion methods.In the fourth chapter,we discusse the fourth root Finsler metric f=A1/4and general fourth root Finsler metric F=(?) and double square roots of Finsler metrics F=(?)+C under the condition of dually flat.we obtain some differential equations these Finsler metrics satisfied,and then give the coefficients of these three Finsler metric’s geodesics.