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

top
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

top

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

top
  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. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.