DOI QR코드

DOI QR Code

ON THE QUATERNIONIC GENERAL HELICES IN EUCLIDEAN 4-SPACE

Yoon, Dae-Won

  • Received : 2012.06.17
  • Accepted : 2012.07.04
  • Published : 2012.09.25

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

References

  1. 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.
  2. K. Bharathi, M. Nagaraj, Quaternion valued function of a real variable Serret- Frenet formulae, Indian J. Pure appl. Math. 16 (1985) 741-756.
  3. 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.
  4. W. K. Clifford, Preliminary sketch of biquaternions, Proc. London Math. Soc. 4 (1873) 361-395.
  5. 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. https://doi.org/10.1016/S0096-3003(03)00783-5
  6. 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. https://doi.org/10.1007/s00006-011-0284-6
  7. M. A. Gungor and M. Tosun, Some characterizations of quaternionic rectifying curves, Differential Geom.-Dynamical Systems 13 (2011) 89-100.
  8. A. Magden, On the curves of constant slope, YYU Fen Bilimleri Dergisi, 4 (1993) 103-109.
  9. H. Kocayigit and M. Onder, Time-like curves of constant slope in Miknkowski space ${\mathbb{E}}_{1}^{4}$ , BU/JST, 1(2007), 311-318.