Normal form and two-dimensional chains of an elliptic CR manifold in \(\mathbb{C}^4\)
type: Item
instance of: scholarly article
title: Normal form and two-dimensional chains of an elliptic CR manifold in \(\mathbb{C}^4\)
zbMATH Open document ID: 0916.32009
DOI: 10.1007/BF02921621
author: Vladimir Ejov
author: Gerd Schmalz
published in: The Journal of Geometric Analysis
publication date: 1998-08-16T00:00:00Z
review text: Let \(M\) be real-analytic CR manifold of codimension 2 in \(\mathbb{C}^4\) with elliptic form, passing through the origin. In analogy with the Chern-Moser normal form of a hypersurface, a construction of the normal form for \(M\) is given in this paper. Furthermore, it is shown that there exist as many such normal forms at a fixed point as there are isotropic automorphisms of the tangent elliptic quadric (Theorem 2). Also the authors prove that the chain-preserving normaliztions of a hypersurface, given in that normal form, must be a fractional linear transformation (Theorem 3).
reviewed by: Tan Vovan
Mathematics Subject Classification ID: 32C05
Mathematics Subject Classification ID: 32V40
zbMATH DE Number: 1191282
zbMATH Keywords: two-dimensional chains
zbMATH Keywords: elliptic CR manifold in \(\mathbb{C}^4\)
zbMATH Keywords: normal forms
MaRDI profile type: Publication
cites work: Real hypersurfaces in complex manifolds
cites work: Q3695580
cites work: Holomorphic automorphisms of quadrics
cites work: Q3705707
cites work: Q3810926
cites work: Q4711776
full work available at URL: https://doi.org/10.1007/bf02921621
OpenAlex ID: W2015777805
description: scientific article; zbMATH DE number 1191282