There are two definitions of Einstein-Finsler spaces introduced by Akbar-Zadeh, which we will show is equal along the integral curves of I-invariant projective vector fields. The sub-algebra of the C-projective vector fields, leaving the H-curvature invariant, has been studied extensively. Here we show on a closed Finsler space with negative definite Ricci curvature reduces to that of Killing vector fields. Moreover, if an Einstein-Finsler space admits such a projective vector field then the flag curvature is constant. Finally, a classification of compact isotropic mean Landsberg manifolds admitting certain projective vector fields is obtained with respect to the sign of Ricci curvature.

由Akbar-Zadeh引入的爱因斯坦-芬斯勒空间有两种定义，我们将证明它们沿着I不变射影矢量场的积分曲线相等。C射影矢量场的子代数，使H曲率不变，已经得到了广泛的研究。在这里，我们展示了在具有负定Ricci曲率的封闭Finsler空间上减小为Killing矢量场的情况。此外，如果爱因斯坦-芬斯勒空间允许这样的投影矢量场，则标志曲率是恒定的。最后，关于Ricci曲率的符号，获得了允许各射影矢量场的紧凑各向同性平均Landsberg流形的分类。