On rectifying curves in Minkowski 3-space
Downloads
DOI:
https://doi.org/10.26637/mjm904/002Abstract
In this study, we investigate the rectifying curve and its centrode by using a dilation of a unit speed curve on pseudo-sphere or pseudo-hyperbolic space. Firstly, considering a causal character of any curve, we study the connection between Serret-Frenet apparatus of the curve on pseudo-sphere or pseudo-hyperbolic space and its dilation. Then, we extend necessary conditions in order to make the centrode a rectifying curve. Also, we examine some properties of centrode which is a rectifying curve.
Keywords:
Rectifying curve, Minkowski 3−space, Frenet equations, centrode, helixMathematics Subject Classification:
53C40, 53C50- Pages: 181-193
- Date Published: 01-10-2021
- Vol. 9 No. 04 (2021): Malaya Journal of Matematik (MJM)
B.Y. C HEN , When does the position vector of a space curve always lie in its rectifying plane?, Am. Math.
Mon., 110(2003), 147–152.
B.Y. Chen And F. Dillen, Rectifying curves as centrodes and extremal curves, Bulletin of the Inst. Math. Academia Sinica, 33(2005), 77-90.
S. Deshmukh, B.Y. Chen and S.H. Alshammari, On rectifying curves in Euclidean 3-space, Turkish J. Math., 42(2018), 609-620.
K. İlARSlan AND E. NEsovic, On rectifying curves as centrodes and extremal curves in the Minkowski 3-spaces, Novi Sad J. Math., 37(2007), 53-64.
K. Ílarslan, E. Nesovic and M.P. Torgasev, Some characterizations of rectifying curves in the Minkowski 3-spaces, Novi Sad J. Math., 33(2003), 23-32.
W. Kunnel, Differential Geometry: Curves-Surfaces-Manifolds, American Mathematical Society, USA, (1999).
B. O’NEILl, Semi Riemann Geometry with Applications to Relativity, Academic Press, London, (1983).
B. Yilmaz, İ. Gök And Y. Yayli, Extended rectifying curves in Minkowski 3-space, Adv. Appl. Clifford Algebras, 26(2016), 861-872.
A. YüCESAn, N. AyyIldiz And A.C. ÇöKen, On rectifying dual space curves, Rev. Mat. Complut., 20(2007), 497-506.
- NA
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 Gülşah AYDIN ŞEKERCİ, Sibel SEVİNÇ, Abdilkadir Ceylan ÇÖKEN
This work is licensed under a Creative Commons Attribution 4.0 International License.
