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Tr. Mat. Inst. Steklova, 2006, Volume 253, Pages 111–126 (Mi tm88)  

This article is cited in 3 scientific papers (total in 3 papers)

On a Family of Lie Algebras Related to Homogeneous Surfaces

A. V. Loboda

Voronezh State Academy of Building and Architecture

Abstract: Real affine homogeneous hypersurfaces of general position in three-dimensional complex space $\mathbb C^3$ are studied. The general position is defined in terms of the Taylor coefficients of the surface equation and implies, first of all, that the isotropy groups of the homogeneous manifolds under consideration are discrete. It is this case that has remained unstudied after the author's works on the holomorphic (in particular, affine) homogeneity of real hypersurfaces in three-dimensional complex manifolds. The actions of affine subgroups $G\subset \mathrm {Aff}(3,\mathbb C)$ in the complex tangent space $T_p^{\mathbb C}M$ of a homogeneous surface are considered. The situation with homogeneity can be described in terms of the dimensions of the corresponding Lie algebras. The main result of the paper eliminates “almost trivial” actions of the groups $G$ on the spaces $T_p^{\mathbb C}M$ for affine homogeneous strictly pseudoconvex surfaces of general position in $\mathbb C^3$ that are different from quadrics.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2006, 253, 100–114

Bibliographic databases:

UDC: 517.5
Received in September 2005

Citation: A. V. Loboda, “On a Family of Lie Algebras Related to Homogeneous Surfaces”, Complex analysis and applications, Collected papers, Tr. Mat. Inst. Steklova, 253, Nauka, MAIK Nauka/Inteperiodika, M., 2006, 111–126; Proc. Steklov Inst. Math., 253 (2006), 100–114

Citation in format AMSBIB
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\by A.~V.~Loboda
\paper On a~Family of Lie Algebras Related to Homogeneous Surfaces
\inbook Complex analysis and applications
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2006
\vol 253
\pages 111--126
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm88}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2338692}
\elib{http://elibrary.ru/item.asp?id=13506631}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2006
\vol 253
\pages 100--114
\crossref{https://doi.org/10.1134/S0081543806020106}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748289440}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. M. Demin, A. V. Loboda, “An Example of a Two-Parameter Family of Affine Homogeneous Real Hypersurfaces in $\mathbb C^3$”, Math. Notes, 84:5 (2008), 737–740  mathnet  crossref  crossref  mathscinet  isi
    2. 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
    3. A. V. Loboda, T. T. D. Nguyẽn, “On the affine homogeneity of tubular type surfaces in $\mathbb C^3$”, Proc. Steklov Inst. Math., 279 (2012), 93–109  mathnet  crossref  mathscinet  isi  elib  elib
  •    . . .  Proceedings of the Steklov Institute of Mathematics
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