The Explicit Structure Of Projectively Flat Finsler Metrics With Three Parameters

Finsler geometry is Riemann geometry without the quadratic re-striction in measure.The geometry master Mr Chern had once said:"The Riemann geometry obtained the huge development in 20th centu-ry,and in the 21st century,it would be the mainstream of the differential geometry".In this paper,the author constructed some class of Finsler metrics with three parameters,got the sufficient and necessary condi-tions of this metrics are projectively flat by studying Hamel equation and the condition of projectively flat.This paper are mainly divided into four parts:1.We mainly gave the basic knowledge of Finsler geometry,dis-cussed the definitions and properties of projectively flat Finsler metric and spherically symmetric projectively flat Finsler metric.2.We manufactured a class of projectively flat Finsler metric with three parameters,got the sufficient and necessary condition of the measurement is projectively flat by using of Hamel equation and flag curvature expression is given.3.We constructed a class of spherically symmetric Finsler metric with three parameters and the sufficient and necessary condition for this kind of metric to be projectively fiat is given.4.We manufactured a class of spherically symmetric Finsler met-ric with constant flag curvature K=0.