On projectivized vector bundles and positive holomorphic sectional curvature

Angelynn Alvarez; Gordon Heier; Fangyang Zheng

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arXiv · 1606.08347

On projectivized vector bundles and positive holomorphic sectional curvature

Angelynn Alvarez·Gordon Heier·Fangyang Zheng

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Abstract

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

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Angelynn Alvarez, Gordon Heier, Fangyang Zheng. 2016-06-27. On projectivized vector bundles and positive holomorphic sectional curvature. https://arxiv.org/abs/1606.08347

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