On the Moser normal form at a non-umbilic point
type: Item
instance of: scholarly article
title: On the Moser normal form at a non-umbilic point
zbMATH Open document ID: 0358.32013
DOI: 10.1007/BF01421918
published in: Mathematische Annalen
publication date: 1978-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/163099
review text: Any analytic real hypersurface \(M^{2n+1}\) in \(\mathbb{C}^{n+1}\), \(n\geq 1\)with non-degenerate Levi form at a point \(p\) has a normal form relative to certain holomorphic coordinate systems centered at \(p\) [\textit{S. S. Chern} and \textit{J. K. Moser}, Acta math. 133 (1974), 219-271 (1975; Zbl 0302.32015)]. The normal form is determined up to the action of a non-compact isotropy group. For \(M^3\subset \mathbb{C}^2\) Moser has given further normalizations which reduce this isotropy group to \(\mathbb{Z}_2\) when \(p\) is a non-umbilic point. In this paper it is shown how to make analogous further normalization at a non-umbilic point when \(m\geq 2\). The isotropy group is reduced to \(U(n) \times \mathbb{Z}_2\). In the generic case it is shown how to reduce the isotropy group to a finite group. The method is to make use of the pseudo-conformal connection and certain normalizations of it carried out by the author in a previous paper.
Mathematics Subject Classification ID: 32C99
Mathematics Subject Classification ID: 32Q99
zbMATH DE Number: 3558195
author: Sidney M. Webster
MaRDI profile type: Publication
cites work: Real hypersurfaces in complex manifolds
cites work: Pseudo-hermitian structures on a real hypersurface
OpenAlex ID: W2027997152
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description: scientific article; zbMATH DE number 3558195