, Volume 82, Issue 1, pp 81-84

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

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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.

Received: 17 December 2002