2004/04/16 by E. Chirka, Евгений Михайлович Чирка, Chirka, E. +2
Mathematics · #32E99 #32L99 #37F75 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #math.CV #math.DS #msc:32E99 #msc:32L99 #msc:37F75
paper · pdf · doi:10.48550/arxiv.math/0404290
5 pages
arxiv created 2004/04/16 · openalex publication_date 2004/04/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.