Flat affine surfaces in \(\mathbb{R}^4\) with flat normal connection
type: Item
instance of: scholarly article
title: Flat affine surfaces in \(\mathbb{R}^4\) with flat normal connection
zbMATH Open document ID: 0968.53010
DOI: 10.1023/A:1005267821555
author: Luc Vrancken
author: M. Magid
published in: Geometriae Dedicata
publication date: 2000-09-13T00:00:00Z
review text: Due to Burstin, Meyer, Nomizu and Vrancken there exists an affine invariant metric on every nondegenerate surface \(M\) in \(\mathbb{R}^4\). Choosing a special transversal plane bundle an equiaffine structure is defined on \(M\). Discussing surfaces with flat induced connection and trivial normal connection a remarkable difference to the codimension one case turns out: There are such surfaces which do not have constant equiaffine normal bundle. The main theorem gives a complete classification of these surfaces.
Mathematics Subject Classification ID: 53A15
zbMATH DE Number: 1505828
zbMATH Keywords: Codazzi equation
zbMATH Keywords: equiaffine normal plane
zbMATH Keywords: equiaffine structure
zbMATH Keywords: trivial normal connection
zbMATH Keywords: equiaffine normal bundle
reviewed by: Friedrich Manhart
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1505828