In this paper, we get an inequality in terms of holomorphic sectional curvature of complex Finsler metrics. As applications, we prove a Schwarz Lemma from a complete Riemannian manifold to a complex Finsler manifold. We also show that a strongly pseudoconvex complex Finsler manifold with semi-positive but not identically zero holomorphic sectional curvature has negative Kodaira dimension under an extra condition.

中文翻译：

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复杂Finsler流形的全纯截面曲率。

在本文中，我们得到了复杂Finsler度量的全纯截面曲率的不等式。作为应用，我们证明了Schwarz Lemma从完整的黎曼流形到复杂的Finsler流形。我们还表明，在额外条件下，具有半正但全零截面曲率不相同的强伪凸复Finsler流形具有负Kodaira尺寸。