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

摘要

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.