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Examples on an extension problem of holomorphic maps and a holomorphic 1- dimensional foliation. (English) Zbl 0718.32014
Let $$\partial B(\epsilon)=\{z\in {\mathbb{C}}^ 2:$$ $$1-\epsilon <\| z\| <j1\}$$. The author constructs:
(1) a complex 3-dimensional manifold M and a holomorphic mapping f: $$\partial B(\epsilon)\to M$$ such that for each point z with $$\| z\| =1-\epsilon$$ there is no neighbourhood W of z such that f extends holomorphically to $$W\cup \partial B(\epsilon);$$
(2) a 1-dimensional holomorphic foliation on P(TM) which shows that a theorem of Nishino is not true in higher codimensions.

##### MSC:
 32D15 Continuation of analytic objects in several complex variables 32A40 Boundary behavior of holomorphic functions of several complex variables
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