In this paper, we consider projective deformation of the geodesic system of Finsler spaces by holonomy invariant functions. Starting with a Finsler spray $S$ and a holonomy invariant function ${\mathcal{P}}$, we investigate the metrizability property of the projective deformation $\widetilde{S}=S-2\unicode[STIX]{x1D706}{\mathcal{P}}{\mathcal{C}}$. We prove that for any holonomy invariant nontrivial function ${\mathcal{P}}$ and for almost every value $\unicode[STIX]{x1D706}\in \mathbb{R}$, such deformation is not Finsler metrizable. We identify the cases where such deformation can lead to a metrizable spray. In these cases, the holonomy invariant function ${\mathcal{P}}$ is necessarily one of the principal curvatures of the geodesic structure.

在本文中，我们通过完整不变函数考虑芬斯勒空间测地线系统的射影变形。从芬斯勒喷雾$S$和完整不变函数 ${\mathcal{P}}$开始，我们研究射影变形$\widetilde{S}=S-2\unicode[STIX]{x1D706}的可度量性属性{\mathcal{P}}{\mathcal{C}}$。我们证明，对于任何完整不变的非平凡函数${\mathcal{P}}$和几乎每个值$\unicode[STIX]{x1D706}\in \mathbb{R}$，这种变形不是芬斯勒可度量的。我们确定了这种变形可能导致可计量喷雾的情况。在这些情况下，完整不变函数${\mathcal{P}}$必然是测地线结构的主曲率之一。