|
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)
References:
PDF file
HTML file
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
\Bibitem{Bel79}
\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
\mathnet{http://mi.mathnet.ru/izv1681}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=534592}
\zmath{https://zbmath.org/?q=an:0456.32015|0412.58010}
\transl
\jour Math. USSR-Izv.
\yr 1980
\vol 14
\issue 2
\pages 223--245
\crossref{https://doi.org/10.1070/IM1980v014n02ABEH001092}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980KM96800001}
Linking options:
http://mi.mathnet.ru/eng/izv1681 http://mi.mathnet.ru/eng/izv/v43/i2/p243
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:
-
A. V. Loboda, “On local automorphisms of real analytic hypersurfaces”, Math. USSR-Izv., 18:3 (1982), 537–559
 -
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
-
A. V. Loboda, “Linearizability of automorphisms of non-spherical surfaces”, Math. USSR-Izv., 21:1 (1983), 171–186
-
A. G. Vitushkin, “Real-analytic hypersurfaces in complex manifolds”, Russian Math. Surveys, 40:2 (1985), 1–35
 -
N. G. Kruzhilin, “Local automorphisms and mappings of smooth strictly pseudoconvex hypersurfaces”, Math. USSR-Izv., 26:3 (1986), 531–552
-
V. V. Ezhov, “On the linearization of automorphisms of a real analytic hypersurface”, Math. USSR-Izv., 27:1 (1986), 53–84
-
V. V. Ezhov, “Linearization of stability groups of a class of hypersurfaces”, Russian Math. Surveys, 41:3 (1986), 203–204
-
V. K. Beloshapka, “Finite-dimensionality of the group of automorphisms of a real-analytic surface”, Math. USSR-Izv., 32:2 (1989), 443–448
-
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
-
A. V. Loboda, “Some invariants of tubular hypersurfaces in $\mathbb C^2$”, Math. Notes, 59:2 (1996), 148–157
-
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
-
A. V. Loboda, “Homogeneous strictly pseudoconvex hypersurfaces in $\mathbb C^3$ with two-dimensional isotropy groups”, Sb. Math., 192:12 (2001), 1741–1761
-
A. V. Loboda, “Homogeneous Real Hypersurfaces in $\mathbb C^3$ with Two-Dimensional Isotropy Groups”, Proc. Steklov Inst. Math., 235 (2001), 107–135
-
V. K. Beloshapka, “Real submanifolds in complex space: polynomial models, automorphisms, and classification problems”, Russian Math. Surveys, 57:1 (2002), 1–41
 -
Michael Eastwood, Alexander Isaev, “Examples of unbounded homogeneous domains in complex space”, Sci China Ser A, 48:s1 (2005), 248
-
Martin Kolář, “Local symmetries of finite type hypersurfaces in ℂ2”, Sci China Ser A, 49:11 (2006), 1633
-
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
-
Kossovskiy I. Shafikov R., “Analytic Differential Equations and Spherical Real Hypersurfaces”, J. Differ. Geom., 102:1 (2016), 67–126
|
| Number of views: |
| This page: | 229 | | Full text: | 80 | | References: | 18 | | First page: | 1 |
|
Terms of Use