The Helix Relation between Two Curves

İLKAY ARSLAN GÜVEN^1, and YUSUF YAYLI²

¹Department of Mathematics, University of Gaziantep, Gaziantep, Turkey

²Department of Mathematics, Ankara University, Ankara, Turkey

Cite this paper:
İLKAY ARSLAN GÜVEN and YUSUF YAYLI. The Helix Relation between Two Curves. Turkish Journal of Analysis and Number Theory. 2013; 1(1):23-25. doi: 10.12691/tjant-1-1-6

Abstract

In this study, we give the relation of being general helix and slant helix of two curves by using the equation between them. Also we find some results and express the characterizations of these curves.

Keywords:
general helix Frenet frame Bertrand mates

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	M. Barros, General helices and a theorem of Lancret, Pro. of the Amer. Math. Soc., 125-5 (1997),1503-1509.
[2]	I.A. Güven, S. Kaya, Y. Yayli, General helix and associated plane curve in Minkowski 3-space, Far East Journal of Math. Sciences, 47-2 (2010), 225-233.
[3]	S. Izumiya and N. Takeuchi, Generic properties of helices and Bertrand curves, J. of Geometry, 74 (2002), 97-109.
[4]	L. Kula and Y. Yayli, On slant helix and its spherical indicatrix, Applied Mathematics and Computation, 169 (2005), 600-607.
[5]	W. Kühnel, Differential Geometry, second ed., Am. Math. Soc., 2006.
[6]	D.J. Struik, Lectures on Classical Differential Geometry, Dover, New York, 1988.
[7]	S. Sy, General helices and other topics in the differential geometry of curves, Master of Sci. in Mathematics, Michigan Technological Uni., 2001.