Some Null Quaternionic Curves in Minkowski Spaces
Some Null Quaternionic Curves in Minkowski Spaces
In this work, we examine null quaternionic rectifying curves and null quaternionic similar curves inMinkowski space3 E1. Also, we defined null quaternionic (1,3)-Bertrand partner curves in4 E1. Thus, wehave characterizations between curvatures of these curves in Minkowski spaces.
___
- 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.
- Cambie, S., Goemans, W., Van Den Bussche, I., Rectifying curves
in the n-dimensional Euclidean space, Turkish Journal of
Mathematics, 2016, 40, 210-223.
- 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.
- Chen, B., Dillen, F., Rectifying Curves as Centrodes and Extremal
Curves, Bulletin of the Instıtute of Mathematics Academia Sinica,
2005, 33, 2, 77-90.
- Çöken, A.C., Tuna, A., On the quaternionic inclined curves in theSemi-Euclidean space
E
4, Applied Mathematics and 2 Computation, 2004, 155, 373-389.
- 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.
- Çöken, A.C., Tuna, A., Serret–Frenet Formulae for Null Quaternionic Curves in Semi Euclidean 4-Space
IR
4
Acta 1 Physica Polonica A, 2015, 128, 2-B, 293-296.
- El-Sabbagh, M.F., Ali, A.T., Similar Curves with Variable
Transformations, Konuralp Journal of Mathematics, 2013, 1, 2,
80–90.
- Grbovic, M., Nesovic, E., Some relations between rectifying and
normalcurvesinMinkowski3-space,Mathematical
Communications, 2012, 17, 655-664.
- Hacisalihoglu, H.H., Hareket Geometrisi ve Kuaterniyonlar
Teorisi, Gazi Üniversitesi, Fen-Edebiyat Fakültesi Yayınları Mat.
1983 No: 2.
- 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.
- Keçilioğlu, O., İlarslan, K., Quaternionic Bertrand Curves in
Euclidean 4-Space, Bulletin of Mathematical Analysis and
Applications, 2013, 5, 3, 27-38.
- Önder, M., Quaternionic Salkowski Curves and Similar Curves,
arXiv:1205.1368 [math.DG].
- Soyfidan, T., Güngör, M., Some Characterizations of Quaternionic
Rectifying Curves in the Semi-Euclidean Space, Honam
Mathematical J. (2016) 36(1) 067-083.
- Yücesan, A., Ayyıldız, N., at al., On Rectifying Dual Space Curves,
Revista Matem´atica Complutense, 2007, 20, 2, 497–506.
- Ward, J.P., Quaternions and Cayley Numbers, Kluwer Academic
Publishers, Boston/London, 1997.