一类新的射影平坦的Finsler度量

On a New Class of Projectively Flat Finsler Metrics

摘要: 利用Hamel射影平坦方程获得了一类新的Finsler度量F=αФ(b²,s)在开子集U⊂Rⁿ上射影平坦的充要条件,此类度量包含了由Bryant构造的Sⁿ上具有正常旗曲率K=1,且测地线为大圆周的Finsler度量.

Abstract: In this paper,we obtain a sufficient and necessary condition for F=αФ(b²,s) to be projectively flat on an open subset U⊂Rⁿ by Hamel's projective flatness equation.The class of Finsler metrics contain Finsler metrics of constant flag curvature K=1 on Sn constructed by R.Bryant,whose geodesics are great circles.