The Möbius geometry of hypersurfaces. II.
type: Item
instance of: scholarly article
title: The Möbius geometry of hypersurfaces. II.
zbMATH Open document ID: 1210.32002
author: Michael Bolt
published in: Michigan Mathematical Journal
publication date: 2011-02-02T00:00:00Z
review text: It is the second part of the paper [Mich. Math. J. 56, No. 3, 603--622 (2008; Zbl 1160.32005)] published by the author recently. The main theorem of the present article states: Let \(M^3 \subset {\mathbb C}^2\) be a non-Levi-flat, three times differentiable hypersurface, and let there is a constant \(\varepsilon\in {\mathbb C},\; |\varepsilon| \not= 0, 1,\) such that, for all \(p\in M\), \[ {\mathcal Q}_{r,p} = \varepsilon {\mathcal L}_{r,p}. \] Then \(M\) is contained in the image of \[ M_{\varepsilon} \equiv \left\{(z_1,z_2) : (z_1 + \overline{z}_1) + |z_2|^2 + {\mathrm{Re}} (\varepsilon z_2^2) = 0\right\} \] under an affine map of the form \(F(z) = A z + b\), where \(0 \not= \det A\in {\mathbb R}\).
Mathematics Subject Classification ID: 32A26
Mathematics Subject Classification ID: 32V05
Mathematics Subject Classification ID: 51B10
zbMATH DE Number: 5843849
zbMATH Keywords: functions of several complex variables
zbMATH Keywords: Möbius transformation
zbMATH Keywords: Cauchy-Fantappiè operator
reviewed by: Sergei V. Rogosin
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1291213962
OpenAlex ID: W4247907709
DOI: 10.1307/MMJ/1291213962
description: scientific article; zbMATH DE number 5843849