Affine Geometry of Space Curves

Details Affine Geometry of Space Curves Affine Geometry of Space Curves

2007-10-14

arxiv.org/abs/0710.2661v3

Differential Geometry - Dynamical Systems, Vol.13, 2011, pp. 191-200

Mathematics

Differential Geometry

17 pages

Scientific paper

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.

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