Hermitian manifolds with nonpositive holomorphic sectional curvature

Kai Tang

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arXiv · 2607.23246

Hermitian manifolds with nonpositive holomorphic sectional curvature

Kai Tang

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Abstract

We study compact K\"ahler manifolds admitting Hermitian metrics with nonpositive holomorphic sectional curvature. We prove that the canonical bundle of such a manifold is nef, removing the pluriclosed assumption from the corresponding nefness result of Broder-Stanfield \cite{BroderStanfield}. In complex dimension two, we further show that negative holomorphic sectional curvature implies the ampleness of the canonical bundle. In complex dimension three, the same conclusion holds if the Hermitian metric is additionally assumed to be balanced. We also prove that vanishing holomorphic sectional curvature forces the first Chern class to vanish.

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BibTeX RIS

Kai Tang. 2026-07-25. Hermitian manifolds with nonpositive holomorphic sectional curvature. https://arxiv.org/abs/2607.23246

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