On the Space of Oriented Affine Lines in $R^3$

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.

3 pages, no figures, AMS-Latex

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