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Izv. RAN. Ser. Mat., 2007, Volume 71, Issue 3, Pages 113–140 (Mi izv2604)  

This article is cited in 1 scientific paper (total in 1 paper)

On envelopes of holomorphy of model manifolds

I. G. Kossovskii

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We construct envelopes of holomorphy for model manifolds of order 4 and describe a class of such manifolds whose envelope is a cylindrical domain (with respect to certain variables) based on a Siegel domain of the second kind. This enables us to prove the holomorphic rigidity of model manifolds of this class. We also study the envelope of holomorphy of a special model manifold of type (1,4) and show it to be a domain of ounded type whose distinguished boundary coincides with the initial manifold. The holomorphic automorphism group of this domain coincides with that of the initial manifold. The envelope of holomorphy is fibred into orbits of this group. The generic orbits are 8-dimensional homogeneous non-spherical completely non-degenerate manifolds in $\mathbb C^5$.

DOI: https://doi.org/10.4213/im2604

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English version:
Izvestiya: Mathematics, 2007, 71:3, 545–571

Bibliographic databases:

UDC: 517.55
MSC: 32V40
Received: 27.12.2006
Revised: 22.01.2007

Citation: I. G. Kossovskii, “On envelopes of holomorphy of model manifolds”, Izv. RAN. Ser. Mat., 71:3 (2007), 113–140; Izv. Math., 71:3 (2007), 545–571

Citation in format AMSBIB
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  • https://doi.org/10.4213/im2604
  • http://mi.mathnet.ru/eng/izv/v71/i3/p113

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Sabzevari M., “Biholomorphic Equivalence to Totally Nondegenerate Model Cr Manifolds”, Ann. Mat. Pura Appl., 198:4 (2019), 1121–1163  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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