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In this paper, geometric properties of spacelike curves on a timelike surface in Lorentz-Minkowski 3-space are investigated by applying the singularity theory of smooth functions from the contact viewpoint.
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We obtain a complete list of simple framed curve singularities in ℂ² and ℂ³ up to the framed equivalence. We also find all the adjacencies between simple framed curves.
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