TY  - JOUR
T1  - Polynomial Parametric Equations of Rectifying Salkowski Curves
AU  - Yılmaz, Beyhan
AU  - Gök, İsmail
AU  - Yaylı, Yusuf
PY  - 2021
DA  - March
DO  - 10.35378/gujs.695460
JF  - Gazi University Journal of Science
PB  - Gazi University
WT  - DergiPark
SN  - 2147-1762
SP  - 211
EP  - 219
VL  - 34
IS  - 1
LA  - en
AB  - 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.
KW  - Rectifying curve
KW  - Salkowski curve
KW  - Harmonic curvature
CR  - [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).
CR  - [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).
CR  - [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).
CR  - [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).
CR  - [5]	Salkowski, E.E., “Zur transformation von raumkurven”, Mathematische Annalen, 66(4): 517-557, (1909).
CR  - [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).
CR  - [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).
CR  - [8]	Oh, Y.M., Seo, Y.L., “A Curve Satisfying    with constant  ”, American Journal of Undergraduate Research, 2(12): 57-62, (2015).
CR  - [9]	Do Carmo, M., “Differential geometry of curves and surfaces”, Prentice-Hall, Upper Saddle Riv. N.J., (1976).
CR  - [10]	O'Neill, B., “Semi-Riemannian Geometry with Application to Relativity”, Academic Press, New York, (1983).
UR  - https://doi.org/10.35378/gujs.695460
L1  - https://dergipark.org.tr/en/download/article-file/985218
ER  -