• 호남수학학술지
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• 제45권4호
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• pp.610-618
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• 2023

In this paper, we obtain (k, m)-type slant helices for a null Cartan curve with the Bishop frame in Minkowski space E⁴₁.

• 호남수학학술지
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• 제41권1호
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• pp.175-183
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• 2019

In this paper, it is investigated Lorentz force equations for $N_1$ and $N_2$-magnetic curves in 3-Dimensional Euclidean space. We give the Lorentz force in the Bishop frame in ${\mathbb{E}}^3$. Then, we obtain a new characterization for a magnetic field V. Also, we also give examples for each curve.

• 호남수학학술지
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• 제40권3호
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• pp.561-576
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• 2018

In this paper, we define null Cartan and pseudo null Bertrand curves in Minkowski space ${\mathbb{E}}^3_1$ according to their Bishop frames. We obtain the necessary and sufficient conditions for pseudo null curves to be Bertand B-curves in terms of their Bishop curvatures. We prove that there are no null Cartan curves in Minkowski 3-space which are Bertrand B-curves, by considering the cases when their Bertrand B-mate curves are spacelike, timelike, null Cartan and pseudo null curves. Finally, we give some examples of pseudo null Bertrand B-curve pairs.