Affine Geometry of Space Curves
Differential Geometry
2012-01-11 v3
Abstract
This paper is devoted to the complete classification of space curves under affine transformations in the view of Cartan's theorem. Spivak has introduced the method but has not found the invariants. Furthermore, for the first time, we propound a necessary and sufficient condition for the invariants. Then, we study the shapes of space curves with constant curvatures in detail and suggest their applications in physics, computer vision and image processing.
Keywords
Cite
@article{arxiv.0710.2661,
title = {Affine Geometry of Space Curves},
author = {Mehdi Nadjafikhah and Ali Mahdipour Shirayeh},
journal= {arXiv preprint arXiv:0710.2661},
year = {2012}
}
Comments
17 pages