We apply the existence and special properties of Gauduchon metrics to give several applications. The first one is concerned with the implications of algebro-geometric nature under the existence of a Hermitian metric with nonnegative holomorphic sectional curvature. The second one is to show the non-existence of holomorphic sections on Hermitian vector bundles under certain conditions. The third one is to give a restriction on the $$ \partial \bar{\partial } $$ ∂ ∂ ¯ -closedness of some real ( n − 1, n − 1)-forms on compact complex manifolds.

中文翻译：

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关于 Gauduchon 度量的一些应用

我们应用 Gauduchon 度量的存在性和特殊属性来给出几个应用程序。第一个涉及在具有非负全纯截面曲率的厄米度量存在下的代数几何性质的含义。第二个是证明在一定条件下 Hermitian 向量丛上不存在全纯截面。第三个是对紧复流形上的一些实数 (n − 1, n − 1)-形式的 $$ \partial \bar{\partial } $$ ∂ ∂ ¯ -闭性给出一个限制。