RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy MIAN:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

This article is cited in 12 scientific papers (total in 12 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.

Full text: PDF file (252 kB)
References: PDF file   HTML file

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

Bibliographic databases:

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, Tr. Mat. Inst. Steklova, 253, Nauka, MAIK Nauka/Inteperiodika, M., 2006, 30–45; Proc. Steklov Inst. Math., 253 (2006), 22–36

Citation in format AMSBIB
\Bibitem{GamKos06}
\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 Tr. Mat. Inst. Steklova
\yr 2006
\vol 253
\pages 30--45
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm81}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2338685}
\elib{http://elibrary.ru/item.asp?id=13528362}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2006
\vol 253
\pages 22--36
\crossref{https://doi.org/10.1134/S0081543806020039}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748328043}


Linking options:
  • http://mi.mathnet.ru/eng/tm81
  • http://mi.mathnet.ru/eng/tm/v253/p30

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. V. K. Beloshapka, “A Counterexample to the Dimension Conjecture”, Math. Notes, 81:1 (2007), 117–120  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. 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
    4. 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
    5. 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
    6. 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
    7. V. K. Beloshapka, “Model-surface method: An infinite-dimensional version”, Proc. Steklov Inst. Math., 279 (2012), 14–24  mathnet  crossref  mathscinet  isi  elib
    8. 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
    9. 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
    10. 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
    11. Sabzevari M., “On the Maximum Conjecture”, Forum Math., 30:6 (2018), 1599–1608  crossref  mathscinet  zmath  isi  scopus
    12. M. A. Stepanova, “Ob avtomorfizmakh CR-podmnogoobrazii kompleksnogo gilbertova prostranstva”, Sib. elektron. matem. izv., 17 (2020), 126–140  mathnet  crossref
  •    . . .  Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:289
    Full text:72
    References:21

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020