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Izv. Akad. Nauk SSSR Ser. Mat., 1979, Volume 43, Issue 2, Pages 243–266 (Mi izv1681)  

This article is cited in 18 scientific papers (total in 18 papers)

On the dimension of the group of automorphisms of an analytic hypersurface

V. K. Beloshapka


Abstract: Let $M$ be a nondegenerate real analytic hypersurface in $\mathbf C^2$, let $\xi\in M$, and let $G_\xi$ consist of the automorphisms of $M$ fixing the point $\xi$. Then, as follows from a theorem of Moser, the real dimension of $G_\xi$ does not exceed 5. Here it is shown that 1) dimensions 2, 3, and 4 cannot be realized, but for 0, 1, and 5 examples are given; 2) if the point $\xi$ is not umbilical, then $G_\xi$ consists of not more than two mappings.
Bibliography: 4 titles.

Full text: PDF file (1669 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1980, 14:2, 223–245

Bibliographic databases:

UDC: 517.5
MSC: 32C05, 53A55
Received: 20.11.1978

Citation: V. K. Beloshapka, “On the dimension of the group of automorphisms of an analytic hypersurface”, Izv. Akad. Nauk SSSR Ser. Mat., 43:2 (1979), 243–266; Math. USSR-Izv., 14:2 (1980), 223–245

Citation in format AMSBIB
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\by V.~K.~Beloshapka
\paper On the dimension of the group of automorphisms of an analytic hypersurface
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1979
\vol 43
\issue 2
\pages 243--266
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\transl
\jour Math. USSR-Izv.
\yr 1980
\vol 14
\issue 2
\pages 223--245
\crossref{https://doi.org/10.1070/IM1980v014n02ABEH001092}
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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. A. V. Loboda, “On local automorphisms of real analytic hypersurfaces”, Math. USSR-Izv., 18:3 (1982), 537–559  mathnet  crossref  mathscinet  zmath
    2. V. K. Beloshapka, A. G. Vitushkin, “Estimates for the radius of convergence of power series defining mappings of analytic hypersurfaces”, Math. USSR-Izv., 19:2 (1982), 241–259  mathnet  crossref  mathscinet  zmath
    3. A. V. Loboda, “Linearizability of automorphisms of non-spherical surfaces”, Math. USSR-Izv., 21:1 (1983), 171–186  mathnet  crossref  mathscinet  zmath
    4. A. G. Vitushkin, “Real-analytic hypersurfaces in complex manifolds”, Russian Math. Surveys, 40:2 (1985), 1–35  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. N. G. Kruzhilin, “Local automorphisms and mappings of smooth strictly pseudoconvex hypersurfaces”, Math. USSR-Izv., 26:3 (1986), 531–552  mathnet  crossref  mathscinet  zmath  isi
    6. V. V. Ezhov, “On the linearization of automorphisms of a real analytic hypersurface”, Math. USSR-Izv., 27:1 (1986), 53–84  mathnet  crossref  mathscinet  zmath
    7. V. V. Ezhov, “Linearization of stability groups of a class of hypersurfaces”, Russian Math. Surveys, 41:3 (1986), 203–204  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. V. K. Beloshapka, “Finite-dimensionality of the group of automorphisms of a real-analytic surface”, Math. USSR-Izv., 32:2 (1989), 443–448  mathnet  crossref  mathscinet  zmath
    9. A. V. Loboda, “Linearizability of holomorphic mappings of generating manifolds of codimension 2 in $\mathbf C^4$”, Math. USSR-Izv., 36:3 (1991), 655–667  mathnet  crossref  mathscinet  zmath  adsnasa
    10. A. V. Loboda, “Some invariants of tubular hypersurfaces in $\mathbb C^2$”, Math. Notes, 59:2 (1996), 148–157  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. A. V. Loboda, “Local Description of Homogeneous Real Hypersurfaces of the Two-Dimensional Complex Space in Terms of Their Normal Equations”, Funct. Anal. Appl., 34:2 (2000), 106–113  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. A. V. Loboda, “Homogeneous strictly pseudoconvex hypersurfaces in $\mathbb C^3$ with two-dimensional isotropy groups”, Sb. Math., 192:12 (2001), 1741–1761  mathnet  crossref  crossref  mathscinet  zmath  isi
    13. A. V. Loboda, “Homogeneous Real Hypersurfaces in $\mathbb C^3$ with Two-Dimensional Isotropy Groups”, Proc. Steklov Inst. Math., 235 (2001), 107–135  mathnet  mathscinet  zmath
    14. V. K. Beloshapka, “Real submanifolds in complex space: polynomial models, automorphisms, and classification problems”, Russian Math. Surveys, 57:1 (2002), 1–41  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    15. Michael Eastwood, Alexander Isaev, “Examples of unbounded homogeneous domains in complex space”, Sci China Ser A, 48:s1 (2005), 248  crossref  mathscinet  zmath
    16. Martin Kolář, “Local symmetries of finite type hypersurfaces in ℂ2”, Sci China Ser A, 49:11 (2006), 1633  crossref  mathscinet  zmath  isi
    17. M. S. Danilov, A. V. Loboda, “Affine Homogeneity of Indefinite Real Hypersurfaces in the Space $\mathbb{C}^3$”, Math. Notes, 88:6 (2010), 827–843  mathnet  crossref  crossref  mathscinet  isi
    18. Kossovskiy I. Shafikov R., “Analytic Differential Equations and Spherical Real Hypersurfaces”, J. Differ. Geom., 102:1 (2016), 67–126  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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