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arXiv · 1507.06629

Optimal pinching for the holomorphic sectional curvature of Hitchin's metrics on Hirzebruch surfaces

Angelynn Alvarez·Ananya Chaturvedi·Gordon Heier
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Abstract

The main result of this note is that, for each $n\in \{1,2,3,\ldots\}$, there exists a Hodge metric on the $n$-th Hirzebruch surface whose positive holomorphic sectional curvature is $\frac{1}{(1+2n)^2}$-pinched. The type of metric under consideration was first studied by Hitchin in this context. In order to address the case $n=0$, we prove a general result on the pinching of the holomorphic sectional curvature of the product metric on the product of two Hermitian manifolds $M$ and $N$ of positive holomorphic sectional curvature.

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Angelynn Alvarez, Ananya Chaturvedi, Gordon Heier. 2015-07-23. Optimal pinching for the holomorphic sectional curvature of Hitchin's metrics on Hirzebruch surfaces. https://arxiv.org/abs/1507.06629

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