Non-lightlike Bertrand W curves: A new approach by system of differential equations for position vector

Ayşe Yavuz; Melek Erdoǧdu; Ayşe Yavuz; Melek Erdoǧdu

doi:10.3934/math.2020348

AIMS Mathematics

2020, Volume 5, Issue 6: 5422-5438. doi: 10.3934/math.2020348

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Research article

Non-lightlike Bertrand W curves: A new approach by system of differential equations for position vector

Ayşe Yavuz ^{1
,
,},
Melek Erdoǧdu ²

1.
Department of Mathematics and Science Education, Necmettin Erbakan University, Konya, 42090, TURKEY
2.
Department of Mathematics, Necmettin Erbakan University, Konya, 42090, TURKEY

Received: 19 April 2020 Accepted: 16 June 2020 Published: 23 June 2020
MSC : 53A35

In this study, the characterization of position vectors belonging to non-lightlike Bertrand W curve mate with constant curvature are obtained depending on differentiable functions. The position vector of Bertrand W curve is stated by a linear combination of its Frenet frame with differentiable functions. There exist also different cases for the curve depending on the value of curvature and torsion. The relationships between Frenet apparatuas of these curves are stated separately for each case. Finally, the timelike and spacelike Bertrand curve mate visualized of given curves as examples, separately.
- W curve,
- Bertrand curve,
- Minkowski space
Citation: Ayşe Yavuz, Melek Erdoǧdu. Non-lightlike Bertrand W curves: A new approach by system of differential equations for position vector[J]. AIMS Mathematics, 2020, 5(6): 5422-5438. doi: 10.3934/math.2020348

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Abstract

In this study, the characterization of position vectors belonging to non-lightlike Bertrand W curve mate with constant curvature are obtained depending on differentiable functions. The position vector of Bertrand W curve is stated by a linear combination of its Frenet frame with differentiable functions. There exist also different cases for the curve depending on the value of curvature and torsion. The relationships between Frenet apparatuas of these curves are stated separately for each case. Finally, the timelike and spacelike Bertrand curve mate visualized of given curves as examples, separately.

References

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