Archiv der Mathematik

, Volume 82, Issue 1, pp 81–84

On the space of oriented affine lines in \( \mathbb{R}^3 \)

Original paper

DOI: 10.1007/s00013-003-4861-3

Cite this article as:
Guilfoyle, B. & Klingenberg, W. Arch. Math. (2004) 82: 81. doi:10.1007/s00013-003-4861-3


We introduce a local coordinate description for the correspondence between the space of oriented affine lines in Euclidean \( \mathbb{R}^3 \) and the tangent bundle to the 2-sphere. These can be utilised to give canonical coordinates on surfaces in \( \mathbb{R}^3 \) , as we illustrate with a number of explicit examples.

Mathematics Subject Classification (1991):

Primary: 51N20Secondary: 53A55.

Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  1. 1.Department of Mathematics and ComputingInstitute of TechnologyTralee Co. KerryIreland
  2. 2.Department of Mathematical SciencesUniversity of DurhamDurhamUnited Kingdom