In this short note, we prove that a complex Finsler vector bundle with positive Kobayashi curvature must be ample, which partially solves a problem of S. Kobayashi posed in 1975. As applications, a strongly pseudoconvex complex Finsler manifold with positive Kobayashi curvature must be biholomorphic to the complex projective space; we also show that all Schur polynomials are numerically positive for complex Finsler vector bundles with positive Kobayashi curvature.

中文翻译：

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具有小林正曲率的复Finsler向量束

在此简短说明中，我们证明了具有小林正曲率的复Finsler向量束必须足够大，这部分解决了1975年提出的S. Kobayashi问题。作为应用，具有小林正曲率的强伪凸复Finsler流形必须是双全纯的到复杂的投影空间；我们还表明，对于具有小林正曲率的复杂Finsler向量束，所有Schur多项式在数值上都是正的。