Let $mathbb{F}^m=(M,F)$ be a Finsler manifold and $G$ be the Sasaki–Finsler metric on the slit tangent bundle $TM^0=TMsetminus{0}$ of $M$. We express the scalar curvature $widetildeho$ of the Riemannian manifold $(TM^0,G)$ in terms of some geometrical objects of the Finsler manifold $mathbb{F}^m$. Then, we find necessary and sufficient conditions for $widetildeho$ to be a positively homogenenous function of degree zero with respect to the fiber coordinates of $TM^0$. Finally, we obtain characterizations of Landsberg manifolds, Berwald manifolds and Riemannian manifolds whose $widetildeho$ satisfies the above condition.
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机译：假设$ mathbb {F} ^ m =（M，F）$为Finsler流形，$ G $为狭缝切线束$ TM ^ 0 = TM setminus {0 } $上的Sasaki–Finsler度量$ M $。我们用芬斯勒流形$ mathbb {F} ^ m $的一些几何对象来表示黎曼流形$（TM ^ 0，G）$的标量曲率$ widetilde rho $。然后，我们发现$ widetilde rho $相对于$ TM ^ 0 $的纤维坐标为零度的正齐次函数的充要条件。最后，我们获得了其 tild rho $满足以上条件的Landsberg流形，Berwald流形和Riemannian流形的刻画。
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