Honam Mathematical Journal (호남수학학술지)

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NOTE ON BERTRAND B-PAIRS OF CURVES IN MINKOWSKI 3-SPACE

  • Received : 2018.05.09
  • Accepted : 2018.08.03
  • Published : 2018.09.25
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Abstract

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.

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References

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