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Mathematics > Differential Geometry

arXiv:0710.2661 (math)
[Submitted on 14 Oct 2007 (v1), last revised 25 Aug 2009 (this version, v3)]

Title:Affine Geometry of Space Curves

Authors:Mehdi Nadjafikhah, Ali Mahdipour Shirayeh
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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.
Comments: 17 pages
Subjects: Differential Geometry (math.DG)
MSC classes: 53A15, 53A04, 53A55
Cite as: arXiv:0710.2661 [math.DG]
  (or arXiv:0710.2661v3 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.0710.2661
Journal reference: Differential Geometry - Dynamical Systems, Vol.13, 2011, pp. 191-200

Submission history

From: Mehdi Nadjafikhah [view email]
[v1] Sun, 14 Oct 2007 14:12:46 UTC (11 KB)
[v2] Sun, 21 Oct 2007 09:21:55 UTC (349 KB)
[v3] Tue, 25 Aug 2009 12:03:56 UTC (13 KB)
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