In this paper, we first give several comparison theorems and their applications in Finsler geometry. Moreover, by means of the Hessian comparison theorems of a real Finsler manifold, Cartan connection, radial flag curvature and tangent curvature, we give Wu’s theorem on a strongly convex weakly Kähler Finsler manifold with a pole. Finally, by using the complex Rund connection and definition of radial flag curvature on a strongly pseudoconvex complex Finsler manifold, we further discuss Wu’s theorem on a strongly convex Kähler Finsler manifold.

中文翻译：

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芬斯勒几何中的比较和吴氏定理

在本文中，我们首先给出几个比较定理及其在 Finsler 几何中的应用。此外，借助实Finsler流形的Hessian比较定理、Cartan连接、径向旗曲率和切线曲率，我们给出了具有极点的强凸弱Kähler Finsler流形的Wu定理。最后，通过使用强赝凸复 Finsler 流形上的复 Rund 连接和径向标志曲率的定义，我们进一步讨论了强凸 Kähler Finsler 流形上的 Wu 定理。