On nonimbeddability of Hartogs figures into complex manifolds

Details On nonimbeddability of Hartogs figures into complex manifolds On nonimbeddability of Hartogs figures into complex manifolds

2004-04-16

arxiv.org/abs/math/0404290v1

Mathematics

Complex Variables

5 pages

Scientific paper

We propose a method to construct examples of strange imbeddings of Hartogs figures into complex manifolds. It gives an imbedding of a "thin" Hartogs figure which does not have any neighborhood biholomorphic to an open set in a Stein manifold, thus unswering a question of E. Poletsky. Then we give an example of a foliated manifold which does not admit any nontrivial imbeddings of a "thick" (i.e. usual) Hartogs figure, giving thus a counterexample to some "selfevident" statements used in foliation theory.

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