The parallel group of a plane curve
de Carvalho, F.J. Craveiro and Robertson, S.A., (1997) The parallel group of a plane curve do Vale, A. Pereira and Pinto, M.R. (eds.) In Proceedings of the 1st International Meeting on Geometry and Topology. European Mathematical Information Service..
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Description/Abstract
For any smooth immersion f of the circle in the plane, the parallel group P(f) consists of all selfdiffeomorphisms of the circle such that the normal lines at points of each orbit are parallel. The action of P(f) on S^1 cannot be transitive. Thus, for example, P(f)\neq SO(2). We construct examples where P(f) contains a subgroup isomorphic to the group of selfdiffeomorphisms of a closed interval (fixing the endpoints), is isomorphic to the cyclic group Z_n for any n\epsilon N, and to the dihedral group D_{n}, for any n\epsilon N. If the curvature of f is nowhere zero, however, then P(f) is cyclic of even order.
Item Type:  Conference or Workshop Item (Paper)  

Venue  Dates:  1st International Meeting on Geometry and Topology, 19970101 

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ePrint ID:  29905  
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Date Deposited:  15 May 2007  
Last Modified:  16 Apr 2017 22:20  
Further Information:  Google Scholar  
URI:  http://eprints.soton.ac.uk/id/eprint/29905 
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