Graphs and their parallel groups (Q1284645)

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.