Hermitian Metrics of Positive Holomorphic Sectional Curvature on Fibrations
Ananya Chaturvedi, Gordon Heier
备注：
This is a pre-print of an article published in Mathematische Zeitschrift. The final authenticated version is available online at: https://doi.org/10.1007/s00209-019-02341-6
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.
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