Mappings preserving some geometrical figures
type: Item
instance of: scholarly article
title: Mappings preserving some geometrical figures
zbMATH Open document ID: 1052.51015
DOI: 10.1023/A:1024668520520
published in: Acta Mathematica Hungarica
publication date: 2004-09-07T00:00:00Z
review text: The author presents the following new characterization of linear isometries of \(\mathbb R^n\) \((n>1)\): If a one-to-one mapping \(f:\mathbb R^n\to \mathbb R^n\) maps the periphery of every regular triangle (quadrilateral or hexagon) of side length \(a>0\) onto the periphery of a figure of the same type with side length \(b>0\), then there exists a linear isometry \(I:\mathbb R^n\to \mathbb R^n\) up to translation such that \(f=(b/a)I\).
Mathematics Subject Classification ID: 51M05
Mathematics Subject Classification ID: 51M04
Mathematics Subject Classification ID: 46B04
zbMATH DE Number: 2098986
zbMATH Keywords: isometry
zbMATH Keywords: characterization of isometries
zbMATH Keywords: Aleksandrov problem
author: Soon-Mo Jung
reviewed by: József Szilasi
MaRDI profile type: Publication
full work available at URL: a:1024668520520
OpenAlex ID: W1928538068
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description: scientific article; zbMATH DE number 2098986