Global uniqueness for ovaloids in Euclidean and affine differential geometry
type: Item
instance of: scholarly article
title: Global uniqueness for ovaloids in Euclidean and affine differential geometry
zbMATH Open document ID: 0761.53008
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1993-04-01T00:00:00Z
review text: Consider an ovaloid in real affine 3-space with relative normalization, with relative metric \(G\) and connection \(\nabla\) (induced by the relative normal). The ovaloid is uniquely determined (modulo affine equivalences) by the connection and the Riemannian volume of \(G\). Euclidean interpretations of this result give the global uniqueness results of Minkowski, Cohn-Vossen and Grove. In equiaffine geometry one needs only \(\nabla\) to determine the ovaloid. A proof in higher dimension is unknown to the author.
Mathematics Subject Classification ID: 53A15
Mathematics Subject Classification ID: 53C45
zbMATH DE Number: 146175
zbMATH Keywords: ovaloid
zbMATH Keywords: relative normalization
zbMATH Keywords: global uniqueness results
zbMATH Keywords: equiaffine geometry
author: Udo Simon
reviewed by: Udo Simon
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227299
OpenAlex ID: W2083949226
Wikidata QID: Q115227252
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DOI: 10.2748/TMJ/1178227299
description: scientific article; zbMATH DE number 146175