Graphs and their parallel groups
type: Item
instance of: scholarly article
title: Graphs and their parallel groups
zbMATH Open document ID: 0918.53001
DOI: 10.1007/BF02844379
publication date: 1999-08-10T00:00:00Z
review text: The authors consider the so-called parallel groups of immersions in Euclidean spaces. The elements of these groups are the self-diffeomorphisms of the domain having the property that the normal vector spaces at the corresponding images under the immersion are preserved (before and after the application of the diffeomorphism). This kind of tangential symmetry of an immersion generalizes the well-studied notions of self-parallelism or transnormality. The main concern of this paper is to determine the parallel groups for some particular classes of immersions and to establish some conditions under which this group can only be trivial. This in particular is done in the case of graphs of maps, illustrating the general features of the notion of parallel groups.
reviewed by: Bernd Wegner
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 1279151
zbMATH Keywords: parallel groups of immersions
zbMATH Keywords: tangential symmetry
zbMATH Keywords: graphs of maps
author: F. J. Craveiro de Carvalho
author: Stewart A. Robertson
MaRDI profile type: Publication
cites work: Q5593095
cites work: Q3679922
cites work: Q4260675
cites work: Parallel Immersions in Euclidean Space
cites work: Q3883164
cites work: Q3999514
cites work: Self-parallel and transnormal curves
published in: Rendiconti del Circolo Matematico di Palermo
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description: scientific article; zbMATH DE number 1279151