具有特殊数量旗曲率的m次根式Finsler度量

M-th Root Finsler Metrics with Special Scalar Flag Curvature

文章研究了具有数量旗曲率的m次根式度量及一般的m次根式F insler度量.证明了此类具有数量旗曲率的F insler度量,若S-曲率是几乎迷向的,那么其旗曲率K为常数.特别地,若度量为m次根式度量,则其旗曲率K为零.

The present paper studies the root metrics and general root metrics with scalar flag curvature. The results prove that if the metrics of this class are with scalar flag curvature and isotropic curvature, then the flag curvature must be constant, especially when the metric is root metric, its flag curvature is zero.