On nonimbeddability of Hartogs figures into complex manifolds
Bulletin de la Société Mathématique de France, Volume 134 (2006) no. 2, p. 261-267

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.

Nous prouvons qu'il est impossible en général de plonger une figure de Hartogs dans une variété complexe proche d'un plongement du disque analytique attaché à une bande totallement réelle. De manière analogue, nous construisons un exemple d'une marmite de Hartogs dans une variété complexe qui n'admet pas un voisignage plongeable dans une variété de Stein.

DOI : https://doi.org/10.24033/bsmf.2509
Classification:  32E10
Keywords: Hartogs figure, holomorphic foliation, Maslov index
@article{BSMF_2006__134_2_261_0,
     author = {Chirka, E. and Ivashkovich, S.},
     title = {On nonimbeddability of Hartogs figures into complex manifolds},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {134},
     number = {2},
     year = {2006},
     pages = {261-267},
     doi = {10.24033/bsmf.2509},
     zbl = {1177.32005},
     mrnumber = {2233708},
     language = {en},
     url = {http://www.numdam.org/item/BSMF_2006__134_2_261_0}
}
Chirka, E.; Ivashkovich, S. On nonimbeddability of Hartogs figures into complex manifolds. Bulletin de la Société Mathématique de France, Volume 134 (2006) no. 2, pp. 261-267. doi : 10.24033/bsmf.2509. http://www.numdam.org/item/BSMF_2006__134_2_261_0/

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