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Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 3, Pages 620–645 (Mi izv2383)  

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

On local automorphisms of real analytic hypersurfaces

A. V. Loboda


Abstract: In this paper the author studies biholomorphic transformations of $\mathbf C^n$ carrying a nondegenerate real analytic surface $M$ into itself and leaving a particular point $\xi\in M$ fixed. The first estimates of the dimensions of such groups of transformations were obtained by V. K. Beloshapka (see Izv. Akad. Nauk SSSR Ser. Mat., 1979, v. 43, № 2, pp. 243–266). In the present paper it is proved that the dimension of such groups for a nonspherical surface $M$ does not exceed $(n-1)^2$.
Bibliography: 2 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1982, 18:3, 537–559

Bibliographic databases:

UDC: 517.5
MSC: Primary 32F25; Secondary 32G10
Received: 21.11.1980

Citation: A. V. Loboda, “On local automorphisms of real analytic hypersurfaces”, Izv. Akad. Nauk SSSR Ser. Mat., 45:3 (1981), 620–645; Math. USSR-Izv., 18:3 (1982), 537–559

Citation in format AMSBIB
\Bibitem{Lob81}
\by A.~V.~Loboda
\paper On local automorphisms of real analytic hypersurfaces
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 3
\pages 620--645
\mathnet{http://mi.mathnet.ru/izv2383}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=623353}
\zmath{https://zbmath.org/?q=an:0488.32014|0473.32016}
\transl
\jour Math. USSR-Izv.
\yr 1982
\vol 18
\issue 3
\pages 537--559
\crossref{https://doi.org/10.1070/IM1982v018n03ABEH001398}


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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. 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
    2. A. G. Vitushkin, “Holomorphic extension of mappings of compact hypersurfaces”, Math. USSR-Izv., 20:1 (1983), 27–33  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. S. M. Ivashkovich, “Extension of locally biholomorphic mappings of domains into complex projective space”, Math. USSR-Izv., 22:1 (1984), 181–189  mathnet  crossref  mathscinet  zmath
    5. A. G. Vitushkin, “Real-analytic hypersurfaces in complex manifolds”, Russian Math. Surveys, 40:2 (1985), 1–35  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. 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
    7. 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
    8. 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
    9. 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
    10. 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
    11. 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
    12. 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
    13. A. V. Loboda, “Homogeneous Nondegenerate Hypersurfaces in $\mathbb{C}^3$ with Two-Dimensional Isotropy Groups”, Funct. Anal. Appl., 36:2 (2002), 151–153  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. Gerd Schmalz, Andrea Spiro, “NORMAL SYSTEMS OF COORDINATES ON MANIFOLDS OF Chern-MOSER TYPE”, Journal of the Korean Mathematical Society, 40:3 (2003), 461  crossref
    15. Bernhard Lamel, Nordine Mir, “Finite jet determination of CR mappings”, Advances in Mathematics, 216:1 (2007), 153  crossref
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