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.

UDC: 517.765+514.765+512.816

Received: 21.03.2011

DOI: 10.4213/faa3111

 English version: Functional Analysis and Its Applications, 2013, 47:2, 113–126

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