English

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

Differential Geometry 2021-11-15 v1

Abstract

We introduce a local coordinate description for the correspondence between the space of oriented affine lines in Euclidean R3{\Bbb{R}}^3 and the tangent bundle to the 2-sphere. These can be utilised to give canonical coordinates on surfaces in R3{\Bbb{R}}^3, as we illustrate with a number of explicit examples.

Keywords

Cite

@article{arxiv.math/0405189,
  title  = {On the Space of Oriented Affine Lines in $R^3$},
  author = {Brendan Guilfoyle and Wilhelm Klingenberg},
  journal= {arXiv preprint arXiv:math/0405189},
  year   = {2021}
}

Comments

3 pages, no figures, AMS-Latex