Affine homogeneity of indefinite real hypersurfaces in the space \(\mathbb C^{3}\)
type: Item
instance of: scholarly article
title: Affine homogeneity of indefinite real hypersurfaces in the space \(\mathbb C^{3}\)
zbMATH Open document ID: 1232.53015
DOI: 10.1134/S0001434610110234
author: M. S. Danilov
author: A. V. Loboda
published in: Mathematical Notes
publication date: 2011-11-25T00:00:00Z
review text: The authors develop a constructive approach to the problem of describing affinely homogeneous real hypersurfaces in 3-dimensional complex space having nondegenerate sign-indefinite Levi form. They 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, the authors 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 in the form of matrix algebras.
reviewed by: Luc Vrancken
Mathematics Subject Classification ID: 53A15
Mathematics Subject Classification ID: 53C56
zbMATH DE Number: 5980727
zbMATH Keywords: affinely homogeneous indefinite hypersurface
zbMATH Keywords: complex space \(\mathbb C^{3}\)
zbMATH Keywords: Lie algebra
zbMATH Keywords: strictly pseudoconvex hypersurface
zbMATH Keywords: Levi form
zbMATH Keywords: Hermitian form
zbMATH Keywords: canonical equation of an indefinite surface
MaRDI profile type: Publication
cites work: Sur la géométrie pseudo-conforme des hypersurfaces de l'espace de deux variables complexes
cites work: Q4938697
cites work: Classification of Levi degenerate homogeneous CR-manifolds in dimension 5
cites work: Local description of homogeneous real hypersurfaces of the two-dimensional complex space in terms of their normal equations
cites work: On a family of affine-homogeneous real hypersurfaces of a three-dimensional complex space
cites work: Real hypersurfaces in complex manifolds
cites work: On affine normal forms and a classification of homogeneous surfaces in affine three-space
cites work: On normal equations of affinely homogeneous convex surfaces of the space \(\mathbb R^3\)
cites work: Q2943181
cites work: Q3265686
cites work: An example of a two-parameter family of affine homogeneous real hypersurfaces in \(\mathbb C^{3}\)
cites work: Q3671396
cites work: Q4200895
full work available at URL: s0001434610110234
OpenAlex ID: W1992708250
description: scientific article; zbMATH DE number 5980727