Rigidity of products
type: Item
instance of: scholarly article
title: Rigidity of products
zbMATH Open document ID: 0778.52014
DOI: 10.1007/BF01263617
author: Irmina Herburt
published in: Geometriae Dedicata
publication date: 1993-12-16T00:00:00Z
review text: A metric space \((X,\rho)\) is called \(GA\) if every two of its points can be joined by an arc of finite length. In this case the intrinsic metric can be considered and shown to be equivalent to the original one. A \(GA\) subset \(Y\) of \(X\) is called rigid in \(X\) if every intrinsic isometry of \(Y\) is the restriction of an isometry of \(X\). The author considers \(GA\)- subsets of Euclidean spaces. She presents an example which shows that rigidity of these subsets is not preserved under standard metric products in general. Furthermore additional topological conditions are developed for these subsets which guarantee that rigidity is presented under products.
Mathematics Subject Classification ID: 52C25
zbMATH DE Number: 205511
zbMATH Keywords: \(GA\)-subsets
zbMATH Keywords: Euclidean spaces
zbMATH Keywords: rigidity
reviewed by: Bernd Wegner
MaRDI profile type: Publication
cites work: ON INTRINSIC ISOMETRIES AND RIGID SUBSETS OF EUCLIDEAN SPACES
cites work: On rigid subsets of some manifolds
description: scientific article; zbMATH DE number 205511