A further characterization of ellipsoids
type: Item
instance of: scholarly article
title: A further characterization of ellipsoids
zbMATH Open document ID: 1089.53008
DOI: 10.1007/BF03322891
author: Luis J. Alías
author: Antonio Gervasio Colares
published in: Results in Mathematics
publication date: 2006-03-07T00:00:00Z
review text: The authors consider a hyperovaloid in unimodular affine space \(\mathbb{A}^{n+1}\). Denote by \(\lambda_1, \dots, \lambda_n\) the affine principal curvatures and by \(L_1,\dots, L_n\) their normed elementary symmetric functions. The authors improve a result from the monograph [\textit{A. M. Li, U. Simon} and \textit{G. Zhao}, Global Affine Differential Geometry of Hypersurfaces. De Gruyter Expositions Math. 11 (1993; Zbl 0808.53002)]; they consider linear relations of the type \[ L_r = \sum_{j=0}^{r-1} C_j L_j \] with real positive constants \(C_j \) to characterize ellipsoids. The proof uses affine Minkowski integral formulas and inequalities for the curvature functions \(L_r\).
Mathematics Subject Classification ID: 53A15
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 5009749
zbMATH Keywords: characterization of ellipsoids
zbMATH Keywords: affine curvature functions
zbMATH Keywords: affine Minkowski integral formulas
reviewed by: Udo Simon
MaRDI profile type: Publication
cites work: Q3262807
cites work: Affine Differential Geometry of Closed Hypersurfaces†
cites work: A characterization of ellipsoids
cites work: Global affine differential geometry of hypersurfaces
cites work: Q3210491
cites work: Q4846450
cites work: Variational properties of functions of the mean curvatures for hypersurfaces in space forms
cites work: Q4271943
cites work: Minkowskische Integralformeln und ihre Anwendungen in der Differentialgeometrie im Großen
full work available at URL: https://doi.org/10.1007/bf03322891
OpenAlex ID: W2085589192
description: scientific article; zbMATH DE number 5009749