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Funktsional. Anal. i Prilozhen., 2013, Volume 47, Issue 2, Pages 38–54 (Mi faa3111)  

Affinely Homogeneous Real Hypersurfaces of $\mathbb{C}^2$

A. V. Loboda

Voronezh State Academy of Building and Architecture

Abstract: A complete affine classification of germs of affinely homogeneous real hypersurfaces of $\mathbb{C}^2$ is presented. The two main tools used in the classification are canonical local equations of manifolds and the theory of Lie algebras. The classification obtained in the paper is shown to be different from the well-known description of holomorphically homogeneous real hypersurfaces of $\mathbb{C}^2$ due to {É.} Cartan (1932).

Keywords: complex space, affine transformation, homogeneous submanifold, vector field, Lie algebra, Levi form, canonical equation of a hypersurface

DOI: https://doi.org/10.4213/faa3111

Full text: PDF file (211 kB)
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English version:
Functional Analysis and Its Applications, 2013, 47:2, 113–126

Bibliographic databases:

UDC: 517.765+514.765+512.816
Received: 21.03.2011

Citation: A. V. Loboda, “Affinely Homogeneous Real Hypersurfaces of $\mathbb{C}^2$”, Funktsional. Anal. i Prilozhen., 47:2 (2013), 38–54; Funct. Anal. Appl., 47:2 (2013), 113–126

Citation in format AMSBIB
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