In this paper we establish partial structure results on the geometry of compact Hermitian manifolds of semipositive Griffiths curvature. We show that after appropriate arbitrary small deformation of the initial metric, the null spaces of the Chern-Ricci two-form generate a holomorphic, integrable distribution. This distribution induces an isometric, holomorphic, almost free action of a complex Lie group on the universal cover of the manifold. Our proof combines the strong maximum principle for the Hermitian Curvature Flow (HCF), new results on the interplay of the HCF and the torsion-twisted connection, and observations on the geometry of the torsion-twisted connection on a general Hermitian manifold.

中文翻译：

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关于具有半正格里菲斯曲率的厄米流形的结构

在本文中，我们建立了半正格里菲斯曲率的紧凑 Hermitian 流形几何的部分结构结果。我们表明，在初始度量适当的任意小变形后，Chern-Ricci 二元形式的零空间生成全纯可积分布。这种分布在流形的普遍覆盖上引起复李群的等距、全纯、几乎自由的作用。我们的证明结合了 Hermitian Curvature Flow (HCF) 的强最大值原理、关于 HCF 和扭扭连接相互作用的新结果，以及对一般厄米流形上扭扭连接几何形状的观察。