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Matematicheskie Zametki, 2010, Volume 88, Issue 6, Pages 867–884
DOI: https://doi.org/10.4213/mzm8563 (Mi mzm8563) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Affine Homogeneity of Indefinite Real Hypersurfaces in the Space C3

M. S. Danilov, A. V. Lobodaa

a Voronezh State Academy of Building and Architecture
Full-text PDF (543 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm8563
Abstract: We develop a constructive approach to the problem of describing affinely homogeneous real hypersurfaces in 3-dimensional complex space having nondegenerate sign-indefinite Levi form. We construct the affine invariants of a nondegenerate indefinite hypersurface in terms of second-order jets of its defining function and introduce the notion of the affine canonical equation of this surface. Three main types of canonical equations are considered. For each of these types, we construct a family of Lie algebras related to affinely homogeneous surfaces of a particular type. As a result, a family (depending on two real parameters) of affinely different homogeneous submanifolds of 3-dimensional complex space is presented (as matrix algebras).
Keywords: affinely homogeneous indefinite hypersurface, complex space C3, Lie algebra, strictly pseudoconvex hypersurface, Levi form, Hermitian form, canonical equation of an indefinite surface.
Received: 20.08.2009
English version:
Mathematical Notes, 2010, Volume 88, Issue 6, Pages 827–843
DOI: https://doi.org/10.1134/S0001434610110234
Bibliographic databases:
Document Type: Article
UDC: 514.142+517.5+512.816.3
Language: Russian
Citation: M. S. Danilov, A. V. Loboda, “Affine Homogeneity of Indefinite Real Hypersurfaces in the Space C3”, Mat. Zametki, 88:6 (2010), 867–884; Math. Notes, 88:6 (2010), 827–843
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm8563
  • https://doi.org/10.4213/mzm8563
  • https://www.mathnet.ru/eng/mzm/v88/i6/p867
    • This publication is cited in the following 6 articles:
    1. A. V. Loboda, “O razmernostyakh grupp affinnykh preobrazovanii, tranzitivno deistvuyuschikh na veschestvennykh giperpoverkhnostyakh v C3”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2014, no. 4(23), 11–35  mathnet
    2. A. V. Loboda, V. K. Evchenko, “Various representations of matrix Lie algebras related to homogeneous surfaces”, Russian Math. (Iz. VUZ), 57:4 (2013), 35–51  mathnet  crossref
    3. T. T. D. Nguen, “Affine-Homogeneous Real Hypersurfaces of Tube Type in C3”, Math. Notes, 94:2 (2013), 238–254  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. A. V. Loboda, “Affinely Homogeneous Real Hypersurfaces of C2”, Funct. Anal. Appl., 47:2 (2013), 113–126  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. Nguen Tkhi Tkhyui Zyong, “Postroenie 5-mernykh matrichnykh algebr li s pomoschyu paketa maple”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2012, no. 1, 162–162  elib
    6. A. V. Loboda, T. T. D. Nguyẽn, “On the affine homogeneity of tubular type surfaces in C3”, Proc. Steklov Inst. Math., 279 (2012), 93–109  mathnet  crossref  mathscinet  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
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