Original paper

Archiv der Mathematik

, Volume 82, Issue 1, pp 81-84

First online:

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

  • B. GuilfoyleAffiliated withDepartment of Mathematics and Computing, Institute of Technology Email author 
  • , W. KlingenbergAffiliated withDepartment of Mathematical Sciences, University of Durham Email author 

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Abstract.

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: 51N20 Secondary: 53A55.