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arXiv:1310.2108 [math.DG]AbstractReferencesReviewsResources

Vortex Filament Equation and Non-Lightlike Space Curves in Minkowski 3-space

Nevin Gürbüz, Süleyman Cengiz

Published 2013-10-08Version 1

In this paper, the parallel transport frames over non-lightlike curves in Minkowski 3-space are introduced. Evolution equations of these frames with respect to arc length and time are calculated over the space of these curves. Then the equivalence of the non-linear Schr\"odinger equation and non-linear heat system to the vortex filament equation for the binormal motion of non-lightlike curves is shown by use of the parallel frames and their evolution equations.

Categories: math.DG, math.DS
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