反全纯向量

本书暂定概念：尚未进入正式概念库。下面是本书给出的定义原文。

定义 · 8.2 复流形上的微积分

现在，$Z\in T_p{M}^{\mathbb{C}}$ 被唯一地分解为 $Z=Z^{+}+Z^{-}$（$Z^{\pm }\in T_p{M}^{\pm }$）。$T_p{M}^{+}$ 由 $\{\partial /\partial z^{\mu }\}$ 张成，而 $T_p{M}^{-}$ 由 $\{\partial /\partial {\overline{z}}^{\mu }\}$ 张成。$Z\in T_p{M}^{+}$ 称为全纯向量(holomorphic vector)，而 $Z\in T_p{M}^{-}$ 称为反全纯向量(anti-holomorphic vector)。我们容易验证

$$T_p{M}^{-}=\overline{T_p{M}^{+}}=\{\bar{Z}|Z\in T_p{M}^{+}\}.\text{\hspace{1em}(8.27)}$$

英文原文

Now $Z\in T_p{M}^{\mathbb{C}}$ is uniquely decomposed as $Z=Z^{+}+Z^{-}$ ( $Z^{\pm }\in T_p{M}^{\pm }$ ). $T_p{M}^{+}$ is spanned by $\{\partial /\partial z^{\mu }\}$ and $T_p{M}^{-}$ by $\{\partial /\partial {\overline{z}}^{\mu }\}$ . $Z\in T_p{M}^{+}$ is called a holomorphic vector while $Z\in T_p{M}^{-}$ is called an anti-holomorphic vector. We readily verify that

$$T_p{M}^{-}=\overline{T_p{M}^{+}}=\{\bar{Z}|Z\in T_p{M}^{+}\}.\text{\hspace{1em}(8.27)}$$

出处：8.2 复流形上的微积分 · node a-34ae3279ad53e63c0fe70687 · 源节点 SHA-256 a32adc06a661338e…