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Dergiler / Turkish Journal of Science / 2026 / Cilt: 6 Sayı: 2

An examination on N − D* partner curves with common principal normal and Darboux vector in E^3.

Süleyman Şenyurt(ORDU ÜNİVERSİTESİ)0000-0003-1097-5541
Şeyda Kılıçoglu(BASKENT UNIVERSITY)0000-0003-0252-1574
Sayfa
89–95
Yayın Tarihi
2021-09-30
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Also we give the Frenet-Serret apparatus of the second curve based on the Frenet-Serret apparatus of first curve.

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Amaç & Hipotez:In this paper we have defined and examined curves with common principal normal and Darboux vectors ; if the principal normal vector of first curve and Darboux vector of second curve are linearly dependent, then first curve has been called N − D* curve, and the second curve is called N − D* partner curve.
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Temel Bulgular & Veri:These new curves are called N − D* pair curves.
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Sonuç & Katkı:Also we give the Frenet-Serret apparatus of the second curve based on the Frenet-Serret apparatus of first curve.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Darboux vector · Offset curves · Mannheim curves

Abstract

In this paper we have defined and examined curves with common principal normal and Darboux vectors ; if the principal normal vector of first curve and Darboux vector of second curve are linearly dependent, then first curve has been called N − D* curve, and the second curve is called N − D* partner curve. These new curves are called N − D* pair curves. Also we give the Frenet-Serret apparatus of the second curve based on the Frenet-Serret apparatus of first curve.

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Bu Makaleye Atıf Yap

Şenyurt, S., Kılıçoglu, Ş. (2021). An examination on N − D* partner curves with common principal normal and Darboux vector in E^3.. Turkish Journal of Science, Cilt: 6 Sayı: 2, 89–95. https://ajindex.com/articles/1557535

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Kaynakça (7)

  1. Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, p. 205, 1997.
  2. Hacisalihoğlu HH. Diferensiyel Geometri, Cilt 1, I´no¨nu¨ U¨ niversitesi Yayinlari, Malatya, 1994.
  3. Lipschutz MM. Schaum’s outline of theory and problems of differential geometry, 1969.
  4. Liu H, Wang F. Mannheim partner curves in 3-space. Journal of Geometry 88(1-2) 2008, 120 – 126.
  5. Schief WK. On the integrability of Bertrand curves and Razzaboni surfaces. Journal of Geometry and Physics, 45(1–2), 2003, 130–150.
  6. Kılıçoğlu, S, Şenyurt, S. An Examination on NP∗ Curves in E3. Turkish Journal of Mathematics and Computer Science, 12(1), 2020, 26–30.
  7. Kılıçoğlu, S, Şenyurt, S. On The Curves N − T ∗ N∗ in E3. Turkish Journal of Mathematics and Computer Science, 12(2), 2020, 161–165.