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Title: Graphs and their parallel groups
Authors: Carvalho, F. Craveiro de 
Robertson, S. 
Issue Date: 1999
Citation: Rendiconti del Circolo Matematico di Palermo. 48:1 (1999) 65-70
Abstract: Abstract Given an immersion of a manifoldf: M?R n+k , dimensionM=n, the parallel groupP(f) off is formed by the diffeomorphisms ofM such that the normalk-planes at points of each orbit are parallel. In [3] we studied the parallel group of a plane closed curve. Here we concentrate on immersionsf: R n ?R n+1, special attention being paid to graphs of smooth maps fromR toR. Graphs of smooth mapsf: S n ?R m are also dealt with and we characterise those maps of which the graph has nontrivial parallel group. To end up we find a sufficient condition for the triviality of the tangent group.
DOI: 10.1007/BF02844379
Rights: openAccess
Appears in Collections:FCTUC Matemática - Artigos em Revistas Internacionais

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