In this paper, we study the generalized Kropina change of generalized m-th root metrics. We find the conditions under which the generalized Kropina change of generalized m-th root metrics to be locally projectively flat and locally dually flat. Further, we find the conditions under which such transformed metric of constant flag curvature reduces to a flat Finsler metric.

中文翻译：

---

广义第m根Finsler度量的广义Kropina变化

在本文中，我们研究了广义第m个根度量的广义Kropina变化。我们找到了广义第m个根度量的广义Kropina变化在局部射影平坦和局部对偶平坦的条件。此外，我们找到了这样的条件，在这种情况下，恒定的标志曲率的这种转换度量减少为平坦的Finsler度量。