论文标题
分布，第一积分和legendrian叶子
Distributions, first integrals and Legendrian foliations
论文作者
论文摘要
我们研究了带有“分离变量”的全体形态分布的细菌。在编纂的一个中，这类分布的一个众所周知的示例是由$ \ Mathbb {p}^{2m+1} $上的规范接触结构给出$（\ mathbb {c}^n，0）$，我们表明存在，对于某些$κ\ in \ mathbb {z} _ {\ geq 0} $，与$ d $的Taylor系数相关（\ Mathbb {C}^κ，0）$，使$ d $在每个级别上都是不可融合的，我们表明，所有级别的$ h_ {d} $ h_ {d} $均包含$ h_ {d percem of z $ p leve， $ z $和$ d $的积分相同。
We study germs of holomorphic distributions with "separated variables'. In codimension one, a well know example of this kind of distribution is given by the canonical contact structure on $\mathbb{P}^{2m+1}$ . Another example is the Darboux distribution, which gives the normal local form of any contact structure. Given a germ $D$ of holomorphic distribution with separated variables in $(\mathbb{C}^n,0)$, we show that there exists , for some $κ\in \mathbb{Z}_{\geq 0}$ related to the Taylor coefficients of $D$, a holomorphic submersion $H_{D}: (\mathbb{C}^n,0) \rightarrow (\mathbb{C}^κ,0)$ such that $D$ is completely non-integrable on each level of $H_{D}$. Furthermore, we show that there exists a holomorphic vector field $Z$ tangent to $D$, such that each level of $H_{D}$ contains a leaf of $Z$ that is somewhere dense in the level. In particular, the field of meromorphic first integrals of $Z$ and that of $D$ are the same.
