an:04183810
Zbl 0718.32014
Kato, Masahide
Examples on an extension problem of holomorphic maps and a holomorphic 1- dimensional foliation
EN
Tokyo J. Math. 13, No. 1, 139-146 (1990).
00156229
1990
j
32D15 32A40
holomorphic extension; boundary behaviour; holomorphic mapping; 1- dimensional holomorphic foliation; theorem of Nishino
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.
M.Jarnicki (Krak??w)