一类新的射影平坦的Finsler度量

摘要

利用Hamel射影平坦方程获得了一类新的Finsler度量F=αФ（b^2，s）在开子集UСR^n上射影平坦的充要条件，此类度量包含了由Bryant构造的S^n上具有正常旗曲率K=1，且测地线为大圆周的Finsler度量．%In this paper, we obtain a sufficient and necessary condition for F = αФ （ b^2, s） to be projectively flat on an open subset UC 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.