On projectivized vector bundles and positive holomorphic sectional curvature

Abstract

We generalize a construction of Hitchin to prove that, given any compact Kähler manifold $M$ with positive holomorphic sectional curvature and any holomorphic vector bundle $E$ over $M$, the projectivized vector bundle $\mathbb{P}(E)$ admits a Kähler metric with positive holomorphic sectional curvature.

Cited by in corpus (4)

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• Hirzebruch manifolds and positive holomorphic sectional curvature
• On real bisectional curvature for Hermitian manifolds
• A note on the almost one half holomorphic pinching