Some Null Quaternionic Curves in Minkowski spaces

Öz

In this work, we examine null quaternionic rectifying curves and null quaternionic similar curves in Minkowski space E1^3. Also, we defined null quaternionic (1,3)-Bertrand partner curves in E1^4. Thus, we have characterizations between curvatures of these curves in Minkowski spaces.

Anahtar Kelimeler

• Null Quaternionic Curve,Rectifying curve,Similar partner curve,Bertrand partner curve

Kaynakça

1. 1. Bharathi, K., Nagaraj, M., Quaternion valued function of a real variable Serret-Frenet formula, Indian Journal of Pure and Applied Mathematic, 1987, 18, 6, 507-511.
2. 2. Cambie, S., Goemans, W., Van Den Bussche, I., Rectifying curves in the n-dimensional Euclidean space, Turkish Journal of Mathematics, 2016, 40, 210-223.
3. 3. Chen, B., When Does the Position Vector of a Space Curve Always Lie in Its Rectifying Plane? American Mathematical Monthly, 2003, 110, 2, 147-152.
4. 4. Chen, B., Dillen, F., Rectifying Curves as Centrodes and Extremal Curves, Bulletin of the Instıtute of Mathematics Academia Sinica, 2005, 33, 2, 77-90.
5. 5. Çöken, A.C., Tuna, A., On the quaternionic inclined curves in the Semi-Euclidean space , Applied Mathematics and Computation, 2004, 155, 373-389.
6. 6. Çöken, A.C., Tuna, A., Null Quaternionic Curves in Semi-Euclidean 3-Space of Index v, Acta Physica Polonica A, 2015, 128, 2-B, 286-289.
7. 7. Çöken, A.C., Tuna, A., Serret–Frenet Formulae for Null Quaternionic Curves in Semi Euclidean 4-Space , Acta Physica Polonica A, 2015, 128, 2-B, 293-296.
8. 8. El-Sabbagh, M.F., Ali, A.T., Similar Curves with Variable Transformations, Konuralp Journal of Mathematics, 2013, 1, 2, 80–90.

9. 9. Grbovic, M., Nesovic, E., Some relations between rectifying and normal curves in Minkowski 3-space, Mathematical Communications, 2012, 17, 655-664.
10. 10. Hacisalihoglu, H.H., Hareket Geometrisi ve Kuaterniyonlar Teorisi, Gazi Üniversitesi, Fen-Edebiyat Fakültesi Yayınları Mat. 1983 No: 2.
11. 11. İlarslan, K., Nesovic, E., Petrovic-Torgasev, M., Some Characterizations of Rectifying Curves in the Minkowski 3–Space, Novi Sad Journal of Mathematics, 2003, 33, 2, 23–32.
12. 12. Keçilioğlu, O., İlarslan, K., Quaternionic Bertrand Curves in Euclidean 4-Space, Bulletin of Mathematical Analysis and Applications, 2013, 5, 3, 27-38.
13. 13. Önder, M., Quaternionic Salkowski Curves and Similar Curves, arXiv:1205.1368 [math.DG].
14. 14. Soyfidan, T., Güngör, M., Some Characterizations of Quaternionic Rectifying Curves in the Semi-Euclidean Space, Honam Mathematical J. (2016) 36(1) 067-083.
15. 15. Yücesan, A., Ayyıldız, N., at al., On Rectifying Dual Space Curves, Revista Matem´atica Complutense, 2007, 20, 2, 497–506.
16. 16. Ward, J.P., Quaternions and Cayley Numbers, Kluwer Academic Publishers, Boston/London, 1997.