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

Yıl 2021, Cilt: 6 Sayı: 2, 89 - 95, 30.09.2021

Süleyman Şenyurt , Şeyda Kılıçoglu

Öz

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.

Anahtar Kelimeler

Darboux vector, Offset curves, Mannheim curves, Bertrand pairs

Kaynakça

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