全纯矢量丛

数学上，全纯矢量丛是指一个在复流形X上的复矢量丛，其全空间E为一复流形，丛投影 $\pi:E\to X$ 是全纯的。重要的全纯矢量丛包括复流形上的全纯切丛，以及其对偶全纯余切丛。一阶全纯矢量丛也称作全纯线丛。

全纯矢量丛的平凡化映射

\phi_U\colon \pi^{-1}(U) \to U\times\mathbb C^k

为双全纯映射。即等价于转换函数

t_{UV}\colon U\cap V \to \mathrm{GL}_k\mathbb C

为全纯映射。

单词	Holomorphic vector bundle
释义	Holomorphic vector bundle 中文百科全纯矢量丛数学上，全纯矢量丛是指一个在复流形X上的复矢量丛，其全空间E为一复流形，丛投影 $\pi:E\to X$ 是全纯的。重要的全纯矢量丛包括复流形上的全纯切丛，以及其对偶全纯余切丛。一阶全纯矢量丛也称作全纯线丛。全纯矢量丛的平凡化映射 $\phi_U\colon \pi^{-1}(U) \to U\times\mathbb C^k$ 为双全纯映射。即等价于转换函数 $t_{UV}\colon U\cap V \to \mathrm{GL}_k\mathbb C$ 为全纯映射。英语百科 Holomorphic vector bundle 全纯向量丛 In mathematics, a holomorphic vector bundle is a complex vector bundle over a complex manifold $X$ such that the total space $E$ is a complex manifold and the projection map $π : E \to X$ is holomorphic. Fundamental examples are the holomorphic tangent bundle of a complex manifold, and its dual, the holomorphic cotangent bundle. A holomorphic line bundle is a rank one holomorphic vector bundle.
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Holomorphic vector bundle