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

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

2004-05-11

arxiv.org/abs/math/0405189v1

Arch. Math. 82 (2004) 81-84

Mathematics

Differential Geometry

3 pages, no figures, AMS-Latex

Scientific paper

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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