Centroaffine first order invariants of surfaces in \(\mathbb{R}^ 4\)
type: Item
instance of: scholarly article
title: Centroaffine first order invariants of surfaces in \(\mathbb{R}^ 4\)
zbMATH Open document ID: 0833.53012
DOI: 10.1007/BF03322278
author: Christine Scharlach
published in: Results in Mathematics
publication date: 1996-03-11T00:00:00Z
review text: The centroaffine differential geometry of oriented surfaces \(M^2\) in \(\mathbb{R}^4 \setminus \{0\}\) is studied using the method of moving frames developed by E. Cartan. Following this method, the author introduces two semiconformal structures on the surface: one is called the affine semiconformal structure (it is related to the Burstin-Mayer metric introduced in the study of nondegenerate equiaffine surfaces in \(\mathbb{R}^4\), see a.o. [\textit{K. Nomizu} and \textit{L. Vrancken}, Int. J. Math. 4, No. 1, 127-165 (1993; Zbl 0810.53006)]) and the other one is called the \(h^3\)-semiconformal structure which is obtained via the Gauss equation. Then, using these structures, a centroaffine metric is introduced and the surfaces are divided into several classes depending on properties of the centroaffine metric and the \(h^3\)-semiconformal structure. Finally, examples are given of surfaces belonging to different classes.
reviewed by: Luc Vrancken
Mathematics Subject Classification ID: 53A15
zbMATH DE Number: 785205
zbMATH Keywords: moving frames method
zbMATH Keywords: centroaffine differential geometry
zbMATH Keywords: affine semiconformal structure
zbMATH Keywords: \(h^ 3\)-semiconformal structure
zbMATH Keywords: centroaffine metric
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03322278
OpenAlex ID: W2029072925
description: scientific article; zbMATH DE number 785205