RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Guidelines for authors License agreement Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Trudy MIAN: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (214 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 517.5

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
\Bibitem{Lob06} \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} 

• http://mi.mathnet.ru/eng/tm88
• http://mi.mathnet.ru/eng/tm/v253/p111

 SHARE:

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. 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
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
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
•  Number of views: This page: 301 Full text: 107 References: 65