A natural Frenet frame for null curves on the lightlike cone in Minkowski space $\mathbb{R} ^{4}_{2}$
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Abstract In this paper, we investigate the representation of curves on the lightlike cone $\mathbb {Q}^{3}_{2}$ Q 2 3 in Minkowski space $\mathbb {R}^{4}_{2}$ R 2 4 by structure functions. In addition, with this representation, we classify all of the null curves on the lightlike cone $\mathbb {Q}^{3}_{2}$ Q 2 3 in four types, and we obtain a natural Frenet frame for these null curves. Furthermore, for this natural Frenet frame, we calculate curvature functions of a null curve, especially the curvature function $\kappa _{2}=0$ κ 2 = 0 , and we show that any null curve on the lightlike cone is a helix. Finally, we find all curves with constant curvature functions.
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2020 ◽
Vol 5
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pp. 237-248
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2019 ◽
Vol 16
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pp. 1950076
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2001 ◽
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pp. 4845-4863
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pp. 1650077
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2009 ◽
Vol 85
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