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 Funktsional. Anal. i Prilozhen.: Year: Volume: Issue: Page: Find

 Funktsional. Anal. i Prilozhen., 2000, Volume 34, Issue 2, Pages 33–42 (Mi faa293)

Local Description of Homogeneous Real Hypersurfaces of the Two-Dimensional Complex Space in Terms of Their Normal Equations

A. V. Loboda

Voronezh State Academy of Building and Architecture

Abstract: In the paper, a classification of real hypersurfaces of the space $\mathbb{C}^2$ that admit transitive actions of local Lie groups of holomorphic transformations is constructed.
Any nonspherical Levi nondegenerate homogeneous surface is determined by the triple of real coefficients $N^2_{520}$, $N_{440}$, $\operatorname{Im}N_{421}$ of a Moser normal equation. All such surfaces are described by several quadratic curves in the space of above coefficients.

DOI: https://doi.org/10.4213/faa293

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English version:
Functional Analysis and Its Applications, 2000, 34:2, 106–113

Bibliographic databases:

UDC: 517.55

Citation: A. V. Loboda, “Local Description of Homogeneous Real Hypersurfaces of the Two-Dimensional Complex Space in Terms of Their Normal Equations”, Funktsional. Anal. i Prilozhen., 34:2 (2000), 33–42; Funct. Anal. Appl., 34:2 (2000), 106–113

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/faa293
• https://doi.org/10.4213/faa293
• http://mi.mathnet.ru/eng/faa/v34/i2/p33

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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. A. V. Loboda, “Homogeneous strictly pseudoconvex hypersurfaces in $\mathbb C^3$ with two-dimensional isotropy groups”, Sb. Math., 192:12 (2001), 1741–1761
2. A. V. Loboda, “Homogeneous Real Hypersurfaces in $\mathbb C^3$ with Two-Dimensional Isotropy Groups”, Proc. Steklov Inst. Math., 235 (2001), 107–135
3. A. V. Loboda, “Homogeneous Nondegenerate Hypersurfaces in $\mathbb{C}^3$ with Two-Dimensional Isotropy Groups”, Funct. Anal. Appl., 36:2 (2002), 151–153
4. A. V. Loboda, “Determination of a Homogeneous Strictly Pseudoconvex Surface from the Coefficients of Its Normal Equation”, Math. Notes, 73:3 (2003), 419–423
5. 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
6. V. I. Sukovykh, “Formuly dlya mladshikh teilorovskikh koeffitsientov odnorodnykh poverkhnostei”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2016, no. 5(36), 104–123
7. A. V. Atanov, A. V. Loboda, V. I. Sukovykh, “On Holomorphic Homogeneity of Real Hypersurfaces of General Position in $\mathbb C^3$”, Proc. Steklov Inst. Math., 298 (2017), 13–34
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