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Mat. Zametki, 2005, Volume 78, Issue 2, Pages 171–179 (Mi mz2574)  

This article is cited in 8 scientific papers (total in 8 papers)

Symmetries of Real Hypersurfaces in Complex 3-Space

V. K. Beloshapka

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

Abstract: The main result of the paper consists in the proof of the fact that for any germ of a real analytic hypersurface in complex 3-space the following alternative (dimension conjecture) takes place: either the dimension of the group of holomorphic symmetries of the germ is at most the dimension of that of a nondegenerate hyperquadric (the latter equals 15), or the group is infinite-dimensional. We also discuss mistakes found in A. Ershova's paper.

DOI: https://doi.org/10.4213/mzm2574

Full text: PDF file (188 kB)
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English version:
Mathematical Notes, 2005, 78:2, 156–163

Bibliographic databases:

UDC: 514.764
Received: 05.07.2004
Revised: 10.12.2004

Citation: V. K. Beloshapka, “Symmetries of Real Hypersurfaces in Complex 3-Space”, Mat. Zametki, 78:2 (2005), 171–179; Math. Notes, 78:2 (2005), 156–163

Citation in format AMSBIB
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    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. V. K. Beloshapka, “A Counterexample to the Dimension Conjecture”, Math. Notes, 81:1 (2007), 117–120  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Fels G., Kaup W., “CR-manifolds of dimension 5: a Lie algebra approach”, J. Reine Angew. Math., 604 (2007), 47–71  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    3. Fels G., Kaup W., “Classification of Levi degenerate homogeneous CR-manifolds in dimension 5”, Acta Math., 201:1 (2008), 1–82  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    4. Isaev A., Zaitsev D., “Reduction of Five-Dimensional Uniformly Levi Degenerate Cr Structures to Absolute Parallelisms”, J. Geom. Anal., 23:3 (2013), 1571–1605  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    5. A. V. Loboda, “O razmernostyakh grupp affinnykh preobrazovanii, tranzitivno deistvuyuschikh na veschestvennykh giperpoverkhnostyakh v $\Bbb C^3$”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2014, no. 4(23), 11–35  mathnet
    6. Beloshapka V.K., Kossovskii I.G., “the Sphere in C-2 as a Model Surface For Degenerate Hypersurfaces in C-3”, Russ. J. Math. Phys., 22:4 (2015), 437–443  crossref  mathscinet  zmath  isi  scopus  scopus
    7. Kolar M., Meylan F., “Nonlinear Cr Automorphisms of Levi Degenerate Hypersurfaces and a New Gap Phenomenon”, Ann. Scuola Norm. Super. Pisa-Cl. Sci., 19:3 (2019), 847–868  crossref  mathscinet  isi
    8. 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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