[KSCI] Korea Science Citation Index Service

Yoon, Dae-Won (Department of Mathematics Education and RINS, Gyeongsang National University)

Publication Information

Abstract

In this paper, we give some characterizations for a quaternionic general helix by means of curvatures of a curve in a 4-dimensional Euclidean space.

Keywords

General helix; Quaternionic curve; Curvature; Frenet frame;

Citations & Related Records

1	K. Bharathi, M. Nagaraj, Quaternion valued function of a real variable Serret- Frenet formulae, Indian J. Pure appl. Math. 16 (1985) 741-756.
2	C. Camci, K. Ilarslan, L. Kula and H. H. Hacisalihoglu, Harmonic curvatures and generalized helices in ${\mathbb{E}}^{n}$ , Chaos, Solitons and Fractals 40 (2007) 1-7.
3	W. K. Clifford, Preliminary sketch of biquaternions, Proc. London Math. Soc. 4 (1873) 361-395.
4	A. C. Coken and A. Tuna, On the quaternionic inclined curves in the semi- Euclidean space ${\mathbb{E}}_{2}^{4}$ , Applied Math. Computation 155 (2004) 373-389. DOI ScienceOn
5	I. Gok, Z. Okuyucu, F. Kahraman and H. H. Hacisalihoglu, On the quaternionic $B_{2}$ -slant helices in the Euclidean space ${\mathbb{E}}^{4}$ , Adv. Appl. Clifford Algebras 21 (2011) 707-719. DOI
6	M. A. Gungor and M. Tosun, Some characterizations of quaternionic rectifying curves, Differential Geom.-Dynamical Systems 13 (2011) 89-100.
7	A. Magden, On the curves of constant slope, YYU Fen Bilimleri Dergisi, 4 (1993) 103-109.
8	H. Kocayigit and M. Onder, Time-like curves of constant slope in Miknkowski space ${\mathbb{E}}_{1}^{4}$ , BU/JST, 1(2007), 311-318.
9	A. T. Ali and R. Lopez, Timelike $B_{2}$ -slant helices in Minkowski space ${\mathbb{E}}_{1}^{4}$ , Arch. Math. (Brno) 46 (2010) 39-46.