Lagrange introduced the notion of Schwarzian derivative and Thurston discovered its mysterious properties playing a role similar to that of curvature on Riemannian manifolds. Here we continue our studies on the development of the Schwarzian derivative on Finsler manifolds. First, we obtain an integrability condition for the Möbius equations. Then we obtain a rigidity result as follows; Let (M, F) be a connected complete Finsler manifold of positive constant Ricci curvature. If it admits non-trivial Möbius mapping, then M is homeomorphic to the n-sphere. Finally, we reconfirm Thurston’s hypothesis for complete Finsler manifolds and show that the Schwarzian derivative of a projective parameter plays the same role as the Ricci curvature on theses manifolds and could characterize a Bonnet–Mayer-type theorem.

拉格朗日引入了 Schwarzian 导数的概念，而 Thurston 发现了它的神秘性质，其作用类似于黎曼流形上的曲率。在这里，我们继续研究 Finsler 流形上 Schwarzian 导数的发展。首先，我们获得了莫比乌斯方程的可积条件。然后我们得到如下的刚性结果；令 ( M ,  F ) 为正常数 Ricci 曲率的连通完备 Finsler 流形。如果它承认非平凡莫比乌斯映射，则M同胚于n-领域。最后，我们再次确认了 Thurston 对完整 Finsler 流形的假设，并表明投影参数的 Schwarzian 导数与这些流形上的 Ricci 曲率起着相同的作用，并且可以表征 Bonnet-Mayer 型定理。