Canonical equiaffine hypersurfaces in \(\mathbb{R}^{n+1}\)
type: Item
instance of: scholarly article
title: Canonical equiaffine hypersurfaces in \(\mathbb{R}^{n+1}\)
zbMATH Open document ID: 0797.53004
DOI: 10.1007/BF02572426
published in: Mathematische Zeitschrift
publication date: 1994-05-10T00:00:00Z
full work available at URL: https://eudml.org/doc/174588
review text: The author defines a canonical hypersurface in real affine space by two conditions: (i) the Blaschke metric is flat, (ii) the cubic form is parallel to the Blaschke metric. Such a hypersurface, in particular, is an affine hypersphere. In case that the index of the Blaschke metric is one, Wang gives a complete classification of canonical hypersurfaces. The method of proof is very interesting: The author reduces this characterization to an algebraic classification problem for commutative, selfadjoint linear operators in a Lorentzian vector space. These operators are defined via the cubic form.
Mathematics Subject Classification ID: 53A15
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 567428
zbMATH Keywords: Blaschke metric
zbMATH Keywords: cubic form
zbMATH Keywords: affine hypersphere
author: Changping Wang
reviewed by: Udo Simon
MaRDI profile type: Publication
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OpenAlex ID: W2088996357
description: scientific article; zbMATH DE number 567428