The University of Southampton
University of Southampton Institutional Repository

The parallel group of a plane curve

Record type: Conference or Workshop Item (Paper)

For any smooth immersion f of the circle in the plane, the parallel group P(f) consists of all self-diffeomorphisms 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 self-diffeomorphisms of a closed interval (fixing the end-points), 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.

Full text not available from this repository.

Citation

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..

More information

Published date: 1997
Venue - Dates: 1st International Meeting on Geometry and Topology, 1997-01-01

Identifiers

Local EPrints ID: 29905
URI: http://eprints.soton.ac.uk/id/eprint/29905
PURE UUID: a37bf3f7-bdaf-4c60-a243-50b2e24c2336

Catalogue record

Date deposited: 15 May 2007
Last modified: 17 Jul 2017 15:56

Export record

Contributors

Author: F.J. Craveiro de Carvalho
Author: S.A. Robertson
Editor: A. Pereira do Vale
Editor: M.R. Pinto

University divisions


Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×