On the quaternionic Mannheim curves of Aw(k)-type in Euclidean space E3

Authors

  • SEZAI KIZILTUĞ Department of Mathematics, Faculty of Science and Arts, Erzincan University, Erzincan, Turkey
  • YUSUF YAYLI Department of Mathematics, Faculty of Sciences, Ankara University, Ankara, Turkey

Keywords:

Aw(k)-type curve, general helix, mannheim curves, quaternion algebra.

Abstract

In this paper, we consider that the curvature conditions of Aw(k)-type (1≤ k ≤ 3) quaternioniccurves in Euclidean space E3 and investigates quaternionic Mannheim curves α:I →Q withk ≠ 0 and r ≠ 0 . Besides, we show that quaternionic Mannheim curves are Aw(2) -type andAw (3)-type quaternionic curves in E3. But, there is no such a Mannheim curve of Aw(1) -type.

Author Biography

SEZAI KIZILTUĞ, Department of Mathematics, Faculty of Science and Arts, Erzincan University, Erzincan, Turkey

Erzincan University, Faculty od Science and Arts, Departments of Mathematic

References

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

Bharathi, K. & Nagaraj, M. 1985. Quaternion valued function of a real Serret-Frenet formulae. Indian Journal of Pure and Applied Mathematics, 16: 741-756.

Çöken, A. C. & Tuna, A. 2004. On the quaternionic inclined curves in the semi-Euclidean space 42 E , Applied Mathematics and Computation 155: 373-389.

Gök, I 307. & Okuyucu, O. Z. & Kahraman, F. & Hacisalihoglu, H. H. 2011. On the Quaternionic B_2-Slant Helices in the Euclidean Space E944, Advances in Applied Clifford Algebras, 21: 707–719.

Karadağ, M.& Sivridağ, A. I

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Published

14-06-2015

Issue

Vol. 42 No. 2 (2015): Kuwait Journal of Science (KJS)

Section

Mathematics