Polynomial Parametric Equations of Rectifying Salkowski Curves

Yıl 2021, Cilt: 34 Sayı: 1, 211 - 219, 01.03.2021

Beyhan Yılmaz , İsmail Gök , Yusuf Yaylı

https://doi.org/10.35378/gujs.695460

Öz

The aim of the paper is to find polynomial parametric equations of rectifying Salkowski curves in Minkowski 3-space, via a serial approach. These curves are characterized by according to their curvature; in particular those curves with constant curvature functions and linear harmonic curvature functions are fully characterized. Then, the equations of the rectifying Salkowski curves are obtained as serial solutions of differential equations with third-order polynomial coefficients.

Anahtar Kelimeler

Rectifying curve, Salkowski curve, Harmonic curvature

Kaynakça

• [1] Chen, B.Y., “When does the position vector of a space curve always lie in its rectifying plane?”, Amer. Math. Monthly, 110: 147-152, (2003).
• [2] Chen, B.Y., “Topics in differential geometry associated with position vector fields on Euclidean submanifolds”, Arab Journal of Mathematical Sciences, 23: 1-17, (2017).
• [3] İlarslan, K., Nesovic, E., Petrovic-Torgasev, M., “Some characterizations of rectifying curves in the Minkowski 3-space”, Novi Sad Journal of Mathematics, 33(2): 23-32, (2003).
• [4] Monterde, J., “Salkowski curves revisited, A family of curves with constant curvature and non-constant torsion”, Computer Aided Geometric Design, 26: 271-278, (2009).
• [5] Salkowski, E.E., “Zur transformation von raumkurven”, Mathematische Annalen, 66(4): 517-557, (1909).
• [6] Yılmaz, B., Metin, Ş., Gök, İ. and Yaylı, Y., “Harmonic curvature functions of some special curves in Galilean 3-space”, Honam Mathematical Journal, 41(2): 301-309, (2019).
• [7] Özdamar, E., Hacisalihoğlu, H.H., “A characterization of inclined curves in Euclidean n-space”, Communication de la facult´e des sciences de L'Universit´e d'Ankara, 24: 15-22, (1975).
• [8] Oh, Y.M., Seo, Y.L., “A Curve Satisfying with constant ”, American Journal of Undergraduate Research, 2(12): 57-62, (2015).
• [9] Do Carmo, M., “Differential geometry of curves and surfaces”, Prentice-Hall, Upper Saddle Riv. N.J., (1976).
• [10] O'Neill, B., “Semi-Riemannian Geometry with Application to Relativity”, Academic Press, New York, (1983).