A Stein Domain with Smooth Boundary Which Has a Product Structure
A Stein Domain with Smooth Boundary Which Has a Product Structure
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具有积结构的光滑边界斯坦因域
DOI：
10.2977/prims/1195183303
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发表时间：
1982
影响因子：
1.2
通讯作者：
T. Ohsawa
中科院分区：
文献类型：
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作者：
T. Ohsawa
众所周知，C中的单位球不是双全纯等价于双圆盘。它的第一个证明是由于H.Cartan[1]，尽管它通常被称为Poincare定理。H.Rischel[3]证明了从严格伪凸域B到乘积域E不存在满射真全纯映射，从而推广了这一定理。最近，A.Huckleberry和E.Ormsby[2]将其推广到B是C“中的有界域且边界光滑且E是全纯纤维丛的全空间的情形。如果B是复流形中边界光滑的相对紧致的Stein域，而E是纤维丛的全空间，那么我们自然会问它是否可以推广到这种情况。本文的目的是给出紧致复流形中的Stein域B的一个例子，它具有以下性质。
It is well known that the unit ball in C is not biholomorphically equivalent to the bidisc. Its first proof is due to H. Cartan [1], although it is customally called Poincare's theorem. H. Rischel [3] extended this theorem by proving that there exists no surjective proper holomorphic map from a strictly pseudoconvex domain B to a product domain E. Recently, A. Huckleberry and E. Ormsby [2] generalized it to the case where B is a bounded domain in C" with smooth boundary and E is the total space of a holomorphic fiber bundle. It will be natural to ask whether we can generalize it to the case where B is a relatively compact Stein domain with smooth boundary in a complex manifold and E is the total space of a fiber bundle. The purpose of the present note is to show an example of a Stein domain B in a compact complex manifold which has the following properties.