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Dergiler / Turkish Journal of Mathematics and Computer Science / 2018 / Cilt: 9 - Sayı: 9

Differential Equations for a Space Curve According to The Unit Darboux Vector

Süleyman Şenyurt
Osman Çakır
Sayfa
91–97
Yayın Tarihi
2022-11-05
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Later, the necessary and sufficient conditions are given for the space curves to be a 1-type Darbouxvector.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this work, the differential equation of a differentiable curve is expressed, by making use of Laplaceand normal Laplace operators, as a linear combination of the unit Darboux vector defined as C = sinϕT + cosϕBof that curve.
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Temel Bulgular & Veri:In this work, the differential equation of a differentiable curve is expressed, by making use of Laplaceand normal Laplace operators, as a linear combination of the unit Darboux vector defined as C = sinϕT + cosϕBof that curve.
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Sonuç & Katkı:Later, the necessary and sufficient conditions are given for the space curves to be a 1-type Darbouxvector.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this work, the differential equation of a differentiable curve is expressed, by making use of Laplaceand normal Laplace operators, as a linear combination of the unit Darboux vector defined as C = sinϕT + cosϕBof that curve. Later, the necessary and sufficient conditions are given for the space curves to be a 1-type Darbouxvector.

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Bu Makaleye Atıf Yap

Şenyurt, S., Çakır, O. (2022). Differential Equations for a Space Curve According to The Unit Darboux Vector. Turkish Journal of Mathematics and Computer Science, Cilt: 9 - Sayı: 9, 91–97. https://ajindex.com/articles/609152

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Kaynakça (9)

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  2. Arslan, K., Kocayiğit, H., Onder, M., Characterizations of space curves with 1-type Darboux instantaneous rotation vector, Commun Korean Math. Soc., 31(2)(2016), 379–388
  3. Chen, B.Y., Ishikawa, S., Biharmonic surface in pseudo-Euclidean spaces, Mem Fac Sci Kyushu Univ Ser A, 45(2)(1991), 323–347
  4. Fenchel, W., On the differential geometry of closed space curves, Bull Amer Math Soc, 57(1951), 44–54
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  6. Ferus, D., Schirrmacher, S., Submanifolds in Euclidean space with simple geodesics, Math Ann., 260(1982), 57–62
  7. Kocayigit, H., Hacısalihoğlu, H.H., 1-type and biharmonic Frenet curves in Lorentzian 3-space, Iran J Sci Tech Trans A Sci, 33(2)(2009), 159-168
  8. Kocayigit, H., Hacısalihoğlu, H.H., 1-type and biharmonic curves in Euclidean 3-space, Int Electron J Geom, 4(1) (2011), 97–101
  9. Struik, D.J., Lectures on Classical Differential Geometry, Dover, GB: 2nd ed, Addison Wesley, 1988.