Graphs and their parallel groups |
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| Authors: | F J Craveiro De Carvalho S A Robertson |
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| Institution: | (1) Departmento de Matemática, Universidade de Coimbra, 3000 Coimbra, Portugal;(2) Faculty of Mathematical Studies, University of Southampton, SO17 IBJ Southampton, UK |
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| 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. |
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| Keywords: | |
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