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A Stein domain with smooth boundary which has a product structure. (English) Zbl 0509.32016

##### MSC:
 32L05 Holomorphic bundles and generalizations 32E10 Stein spaces, Stein manifolds
##### Keywords:
Stein domain; product structure; disc bundle
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##### References:
 [1] Cartan, H., Les fonctions de deux variables complexes et le probleme de la representa- tion analytique, /. Math. Pure et Appl 9e serie 10, (1931), 1-114. · Zbl 0001.28501 · eudml:234639 [2] Huckleberry, A. and Ormsby, E., Nonexistence of proper holomorphic maps between certain complex manifolds, Manuscripta Math. 26 (1978/79), 371-379. · Zbl 0422.32009 · doi:10.1007/BF01170261 · eudml:154595 [3] Rischel, H., Holomorphe Uberlagerungskorrespondenzen, Math. Scand. 15 (1964), 49-63. Added in proof: Recently, Diederich and Fornaess constructed in an analoguous way a domain with smooth pseudoconvex boundary D in P1xHopf surface, and showed that D cannot be exhausted by pseudoconvex subdomains. In fact, D is biholomorphic to (C2{0)X an annulus !
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