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

Hermitian Metrics of Positive Holomorphic Sectional Curvature on Fibrations