On nonimbeddability of Hartogs figures into complex manifolds

E. Chirka; S. Ivashkovich

Bulletin de la Société Mathématique de France (2006)

  • Volume: 134, Issue: 2, page 261-267
  • ISSN: 0037-9484

Abstract

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We prove the impossibility of imbeddings of Hartogs figures into general complex manifolds which are close to an imbedding of an analytic disc attached to a totally real collar. Analogously we provide examples of the so called thin Hartogs figures in complex manifolds having no neighborhood biholomorphic to an open set in a Stein manifold.

How to cite

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Chirka, E., and Ivashkovich, S.. "On nonimbeddability of Hartogs figures into complex manifolds." Bulletin de la Société Mathématique de France 134.2 (2006): 261-267. <http://eudml.org/doc/272449>.

@article{Chirka2006,
abstract = {We prove the impossibility of imbeddings of Hartogs figures into general complex manifolds which are close to an imbedding of an analytic disc attached to a totally real collar. Analogously we provide examples of the so called thin Hartogs figures in complex manifolds having no neighborhood biholomorphic to an open set in a Stein manifold.},
author = {Chirka, E., Ivashkovich, S.},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Hartogs figure; holomorphic foliation; Maslov index},
language = {eng},
number = {2},
pages = {261-267},
publisher = {Société mathématique de France},
title = {On nonimbeddability of Hartogs figures into complex manifolds},
url = {http://eudml.org/doc/272449},
volume = {134},
year = {2006},
}

TY - JOUR
AU - Chirka, E.
AU - Ivashkovich, S.
TI - On nonimbeddability of Hartogs figures into complex manifolds
JO - Bulletin de la Société Mathématique de France
PY - 2006
PB - Société mathématique de France
VL - 134
IS - 2
SP - 261
EP - 267
AB - We prove the impossibility of imbeddings of Hartogs figures into general complex manifolds which are close to an imbedding of an analytic disc attached to a totally real collar. Analogously we provide examples of the so called thin Hartogs figures in complex manifolds having no neighborhood biholomorphic to an open set in a Stein manifold.
LA - eng
KW - Hartogs figure; holomorphic foliation; Maslov index
UR - http://eudml.org/doc/272449
ER -

References

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  1. [1] M. Brunella – On entire curves tangent to a foliation, Preprint, 2004. Zbl1147.32019MR2413062
  2. [2] H. Hofer, V. Lizan & J.-C. Sikorav – « On genericity for holomorphic curves in four-dimensional almost-complex manifolds », J. Geom. Anal.7 (1998), p. 149–159. Zbl0911.53014MR1630789
  3. [3] S. Ivashkovich – « The Hartogs-type extension theorem for meromorphic mappings into compact Kähler manifolds », Invent. Math109 (1992), p. 47–54. Zbl0738.32008MR1168365
  4. [4] —, « Extension properties of meromorphic mappings with values in non-Kähler complex manifolds », Ann. of Math.160 (2004), p. 795–837. Zbl1081.32010MR2144969
  5. [5] E. Poletsky – Private communication. 
  6. [6] F. Sarkis – « On nonimbeddability of topologically trivial domains and thin Hartogs figures of ℙ 2 ( ℂ ) into Stein spaces », 2004, math.CV/0411083. 

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