Examples on an Extension Problem of Holomorphic Maps and a Holomorphic 1-Dimensional Foliation
Examples on an Extension Problem of Holomorphic Maps and a Holomorphic 1-Dimensional Foliation
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全纯映射和全纯一维叶状结构的可拓问题示例
DOI：
10.3836/tjm/1270133009
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发表时间：
1990
影响因子：
0.6
通讯作者：
Masahide Kato
中科院分区：
文献类型：
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作者：
Masahide Kato
$f$：$\Partial B(\epsilon)\右目标M$使得$\Partial B(\epsilon)$的内界$\Sigma_{2}$是$f$的自然边界。也就是说，对于Sigma_{2}$中的任意点$x，我们不能在$C^{2}$中找到$x$的任何邻域$W$，使得$f$可以扩张到从$W\cup\Partial B(\epsilon)$到$M$的全纯映射。其次，我们研究了切丛$TM$的伴随射影丛$P(TM)$上的L维全纯叶层。我们将证明在$P(TM)$中有一个子域$W，$$P(TM)-[W]\neq\Emptyset$，以及$P(TM)-[W]$的一个薄子集$S$，使得$W$中的每个叶都双全纯到$P^{1}$，并且$[W]$之外的所有紧叶都包含在
$f$ : $\partial B(\epsilon)\rightarrow M$ such that the inner boundary $\Sigma_{2}$ of $\partial B(\epsilon)$ is a natural boundary of $f$. That is, for any point $x\in\Sigma_{2}$ , we cannot find any neighborhood $W$ of $x$ in $C^{2}$ such that $f$ can be extended to a holomorphic map of $W\cup\partial B(\epsilon)$ into $M$. Secondly, we study a l-dimensional holomorphic foliation on the associated projective bundle $P(TM)$ of the tangent bundle $TM$. We shall show that in $P(TM)$ there are a subdomain $W,$ $ P(TM)-[W]\neq\emptyset$ , and a thin subset $S$ of $P(TM)-[W]$ such that every leaf in $W$ is biholomorphic to $P^{1}$ and all compact leaves outside $[W]$ are contained in