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

Brendan Guilfoyle·Wilhelm Klingenberg
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Abstract

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

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Brendan Guilfoyle, Wilhelm Klingenberg. 2004-05-11. On the Space of Oriented Affine Lines in $R^3$. https://doi.org/10.1007/s00013-003-4861-3

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