Article Detail

On the quaternionic Bertrand curves of AW(k)-type in Euclidean space E³

SEZAİ KIZILTUĞ

Published Online : 25 Dec 2019

Article Views: 44 | Article Download: 33 Full PDF

Abstract

In this paper, We consider that the curvature conditions of AW(k)-type (1≤k≤3) quaternionic curves in Euclidean space E³ and investigates quaternionic Bertrand curves α : I→Q with k≠0 and r≠0. Besides, we show that quaternionic Bertrand curves to be AW(2)-type and AW(3)-type quaternionic curves in E³. But it is shown that there is no such a quaternionic Bertrand curve of AW(1)-type.

Keywords : AW(k)-type curve, General helix, Bertrand curves, Euclidean space, Quaternion algebra.

References

[1] A. C. Çöken, A. Tuna, On the quaternionic inclined curves in the semi-Euclidean space E₂⁴, Appl. Math. Computation, 155, (2004), 373-389.

[2] C. Özgür, F. Gezgin, On some curves of AW(k)-type, Differ. Geom. Dyn. Syst, 7, (2005) , 74--80.

[3] Ç. Camcı, K. İlarslan, L. Kula, H.H. Hacısalihoğlu, Harmonic curvatures and generalized helices in Eⁿ, Chaos Solitons & Fractals, (2009), 40(5):2590--6.

[4] E. Ata, Y. Yaylı, Dual quaternions and dual projective spaces, Chaos Solitons & Fractals 40, (2009), 15(3):1255-1263.

[5] E. Ata, Y. Yaylı, Split quaternions and semi-Euclidean projective spaces, Chaos Solitons & Fractals 41, (2009), 30(4):1910-1915.

[6] F. Kahraman, İ. Gök, H.H. Hacısalihoğlu, On the quaternionic B₂-Slant Helices in the semi-Euclidean Space E₂⁴, Appl. Math. Computation, 218, (2012), 6391-6400.

[7] İ. Gök İ, O. Z. Okuyucu, F. Kahraman and H. H. Hacisalihoğlu, On the Quaternionic B₂-Slant Helices in the Euclidean Space E⁴, Adv. Appl. Clifford Algebras, 21 (2011), 707--719.

[8] K. Arslan, C. Özgür, Curves and surfaces of AW(k)-type, Geometry and Topology of Submanifolds, IX (Valenciennes/Lyan/Leuven,1997), World. Sci. Publishing, River Edge, NJ, (1999), pp. 21--26.

[9] K. Bharathi, M. Nagaraj, Quaternion valued function of a real Serret-Frenet formulae, Indian J. Pure Appl. Math, 16, (1985), 741-756.

[10] M. Karadağ, A.İ. Sivridağ, Kuaterniyonik Eğilim Çizgileri için karakterizasyonlar, Erc. Ünv. Fen Bil. Derg. 13 1-2, (1997), 37-53.

[11] M. Külahcı, M. Bektas, M. Ergüt, Curves of AW(k)-type in 3-dimensional null cone, Physics Letters A 371, (2007), 275-277.

[12] M. Külahcı, M. Bektas, M. Ergüt, On harmonic curvatures of a Frenet curve in Lorentzian space, Chaos Solitons & Fractals 41, (2009), 1668--1675.

[13] S. Izumiya, N. Takeuchi, Generic properties of helices and Bertrand curves, J. Geom., 74, (2002), 97--109.

[14] S. Izumiya, N. Takeuchi, New special curves and developable surfaces, Turkish J. Math., 28 (2), (2004), 153--163.

[15] S. Kızıltuğ, Y. Yaylı, Bertrand curves of AW(k)-type in according to the Equiform Geometry of the Galilean Space, Abstract and Applied Analysis Volume, (2014), Article ID 402360, 6 pages.

[16] S. Kızıltuğ, Y. Yaylı, On the quaternionic Mannheim curves of Aw(k)-type in Euclidean space E³, 42(2), (2015).

Quick Links Journal Archive Most Downloaded Most Viewed Copyright

Recently Published Issues Some Ps Diophantine Triples for Especial s Integer
Volume 3 Issue 1
2020 The Directional Curves of Frenet Spacelike and Timelike Curves in E_1^3
Volume 2 Issue 3
2019 On the quaternionic Bertrand curves of AW(k)-type in Euclidean space E³
Volume 2 Issue 3
2019