The main result of this note essentially is that if the base and fibers of a compact fibration carry Hermitian metrics of positive holomorphic sectional curvature, then so does the total space of the fibration. The proof is based on the use of a warped product metric as in the work by Cheung in case of negative holomorphic sectional curvature, but differs in certain key aspects, e.g., in that it does not use the subadditivity property for holomorphic sectional curvature due to Grauert-Reckziegel and Wu.

中文翻译：

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纤维上正全纯截面曲率的厄米度量

这篇笔记的主要结果是，如果紧密纤维化的基部和纤维携带正全纯截面曲率的厄米度量，那么纤维化的总空间也是如此。该证明基于 Cheung 在负全纯截面曲率的情况下的工作中使用翘曲乘积度量，但在某些关键方面有所不同，例如，由于全纯截面曲率，它不使用次可加性属性Grauert-Reckziegel 和吴。