SOME CHARACTERIZATIONS OF SLANT AND SPHERICAL HELICES DUE TO SABBAN FRAME

Year 2015, , 64 - 73, 30.10.2015

Bülent Altunkaya , Levent Kula

https://doi.org/10.36753/mathenot.421333

Cited By: 2

Abstract

In this paper, we are investigating that under which conditions of
the geodesic curvature of unit speed curve γ that lies on the unit sphere, the
curve c which is obtained by using γ, is a spherical helix or slant helix.

Keywords

Helices, Spherical Helices, Slant Helices, Sabban Frame

References

• [1] L. Kula, Y. Yaylı, On slant helix and its spherical indicatrix, Appl. Math. Comput., 169 (1), 600-607, 2005.
• [2] S. Izumiya, N. Takeuchi, Generic properties of helices and Bertrand curves , J. Geom. 74, 97-109, 2002.
• [3] R. Encheva, G. Georgiev, Shapes of space curves, Journal for Geometry and Graphics, Vol 7, No. 2, 145-155, 2003.
• [4] S. Izumiya, N. Takeuchi, New special curves and developable surfaces, Turk. J. Math. 28, 153-163, 2004.
• [5] B. O’Neill, Elementary Differential Geometry, Academic Press, 2006.
• [6] D. J. Struik, Lectures on Classical Differential Geometry, Dover, 1961.