Convex surfaces which intersect each congruent copy of themselves in a connected set
type: Item
instance of: scholarly article
title: Convex surfaces which intersect each congruent copy of themselves in a connected set
zbMATH Open document ID: 0601.52001
DOI: 10.1007/BF02764878
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: A convex body \(K\subset {\mathbb{R}}^ 3\) has the intersection property, if for every isometry \(\rho\) of \({\mathbb{R}}^ 3\), the intersection of the boundaries of K and \(\rho\) K is connected. A set \(Y\subset {\mathbb{R}}^ 3\) is the parallel body of a compact convex set X, if there is a Euclidean ball B with the origin as centre, such that \(Y=X+B\). The author presents the following pretty result: If a convex body \(K\subset {\mathbb{R}}^ 3\) has the intersection property, then it is either a Euclidean ball or a parallel body of a line segment.
reviewed by: T. Bisztriczky
Mathematics Subject Classification ID: 52A15
Mathematics Subject Classification ID: 51N20
zbMATH DE Number: 3969529
zbMATH Keywords: convex body
zbMATH Keywords: intersection property
zbMATH Keywords: isometry
zbMATH Keywords: parallel body
zbMATH Keywords: Euclidean ball
author: P. Mani-Levitska
MaRDI profile type: Publication
cites work: Q5801057
cites work: Q5593766
cites work: Connectivity and freely rolling convex bodies
cites work: Q5547252
cites work: Seitenrisse honvexer Körper und Homothetic
cites work: Q5510123
full work available at URL: https://doi.org/10.1007/bf02764878
OpenAlex ID: W2033192657
description: scientific article; zbMATH DE number 3969529