Let $M$ and $N$ be two compact complex manifolds. We show that if the tautological line bundle ${\mathcal{O}}_{T_{M}^{\ast }}(1)$ is not pseudo-effective and ${\mathcal{O}}_{T_{N}^{\ast }}(1)$ is nef, then there is no non-constant holomorphic map from $M$ to $N$. In particular, we prove that any holomorphic map from a compact complex manifold $M$ with RC-positive tangent bundle to a compact complex manifold $N$ with nef cotangent bundle must be a constant map. As an application, we obtain that there is no non-constant holomorphic map from a compact Hermitian manifold with positive holomorphic sectional curvature to a Hermitian manifold with non-positive holomorphic bisectional curvature.

中文翻译：

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全纯映射的 RC 正定性、消失定理和刚性

让$M$和$N$是两个紧凑的复流形。我们证明如果重言式线丛${\mathcal{O}}_{T_{M}^{\ast }}(1)$不是伪有效的并且${\mathcal{O}}_{T_{N}^{\ast }}(1)$是 nef，则不存在来自的非常量全纯映射$M$到$N$. 特别是，我们证明了任何来自紧复流形的全纯映射$M$具有 RC 正切丛的紧凑复流形$N$与 nef 余切丛必须是一个常数映射。作为一个应用程序，我们从一个紧致中得到不存在非常量全纯映射厄米流形和正全纯截面曲率到具有非正全纯二等分曲率的 Hermitian 流形。