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Trudy Mat. Inst. Steklova, 2006, Volume 253, Pages 30–45 (Mi tm81)  

This article is cited in 15 scientific papers (total in 15 papers)

The Envelope of Holomorphy of a Model Third-Degree Surface and the Rigidity Phenomenon

R. V. Gammel', I. G. Kossovskii

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

Abstract: The structures of the graded Lie algebra $\mathop{\mathrm{aut}}Q$ of infinitesimal automorphisms of a cubic (a model surface in $\mathbb C^N$) and the corresponding group $\mathop{\mathrm{Aut}}Q$ of its holomorphic automorphisms are studied. It is proved that for any nondegenerate cubic, the positively graded components of the algebra $\mathop{\mathrm{aut}}Q$ are trivial and, as a consequence, $\mathop{\mathrm{Aut}}Q$ has no subgroups consisting of nonlinear automorphisms of the cubic that preserve the origin (the so-called rigidity phenomenon). In the course of the proof, the envelope of holomorphy for a nondegenerate cubic is constructed and shown to be a cylinder with respect to the cubic variable whose base is a Siegel domain of the second kind.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2006, 253, 22–36

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UDC: 517.55+514.748
Received in December 2005

Citation: R. V. Gammel', I. G. Kossovskii, “The Envelope of Holomorphy of a Model Third-Degree Surface and the Rigidity Phenomenon”, Complex analysis and applications, Collected papers, Trudy Mat. Inst. Steklova, 253, Nauka, MAIK Nauka/Inteperiodika, M., 2006, 30–45; Proc. Steklov Inst. Math., 253 (2006), 22–36

Citation in format AMSBIB
\by R.~V.~Gammel', I.~G.~Kossovskii
\paper The Envelope of Holomorphy of a~Model Third-Degree Surface and the Rigidity Phenomenon
\inbook Complex analysis and applications
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2006
\vol 253
\pages 30--45
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\jour Proc. Steklov Inst. Math.
\yr 2006
\vol 253
\pages 22--36

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    This publication is cited in the following articles:
    1. Sabzevari M. Spiro A., “On the Geometric Order of Totally Nondegenerate Cr Manifolds”, Math. Z.  crossref  mathscinet  isi
    2. I. G. Kossovskii, “On envelopes of holomorphy of model manifolds”, Izv. Math., 71:3 (2007), 545–571  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. V. K. Beloshapka, “A Counterexample to the Dimension Conjecture”, Math. Notes, 81:1 (2007), 117–120  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. V. K. Beloshapka, “Representation of the Group of Holomorphic Symmetries of a Real Germ in the Symmetry Group of Its Model Surface”, Math. Notes, 82:4 (2007), 461–463  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Beloshapka V.K., “A CR-manifold in general position as an \{e\}-structure”, Russ. J. Math. Phys., 14:1 (2007), 1–7  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. Beloshapka V.K., “Representation of the group of holomorphic symmetries of a real germ in the symmetry group of the model surface of the germ”, Russ. J. Math. Phys., 14:2 (2007), 213–215  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    7. Mamai I.B., “Model CR-manifolds with one-dimensional complex tangent”, Russ. J. Math. Phys., 16:1 (2009), 97–102  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    8. V. K. Beloshapka, “Model-surface method: An infinite-dimensional version”, Proc. Steklov Inst. Math., 279 (2012), 14–24  mathnet  crossref  mathscinet  isi  elib
    9. Sabzevari M., Hashemi A., Alizadeh B.M., Merker J., “Lie algebras of infinitesimal CR automorphisms of weighted homogeneous and homogeneous CR-generic submanifolds of CN”, Filomat, 30:6 (2016), 1387–1411  crossref  mathscinet  zmath  isi  elib  scopus
    10. Kolar M., Kossovskiy I., Zaitsev D., “Normal Forms in Cauchy-Riemann Geometry”, Analysis and Geometry in Several Complex Variables, Contemporary Mathematics, 681, eds. Berhanu S., Mir N., Straube E., Amer Mathematical Soc, 2017, 153–177  crossref  mathscinet  zmath  isi  scopus
    11. Beloshapka V.K., “Cubic Model Cr-Manifolds Without the Assumption of Complete Nondegeneracy”, Russ. J. Math. Phys., 25:2 (2018), 148–157  crossref  mathscinet  isi  scopus
    12. Sabzevari M., “On the Maximum Conjecture”, Forum Math., 30:6 (2018), 1599–1608  crossref  mathscinet  zmath  isi  scopus
    13. Sabzevari M., “Biholomorphic Equivalence to Totally Nondegenerate Model Cr Manifolds”, Ann. Mat. Pura Appl., 198:4 (2019), 1121–1163  crossref  mathscinet  isi
    14. M. A. Stepanova, “Ob avtomorfizmakh CR-podmnogoobrazii kompleksnogo gilbertova prostranstva”, Sib. elektron. matem. izv., 17 (2020), 126–140  mathnet  crossref
    15. Beloshapka V.K., “Cr-Manifolds of Finite Bloom-Graham Type: the Model Surface Method”, Russ. J. Math. Phys., 27:2 (2020), 155–174  crossref  mathscinet  isi
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