General helices that lie on the sphere $S^{2n}$ in Euclidean space $E^{2n+1}$

Year 2018, , 166 - 170, 30.09.2018

Bülent Altunkaya , Levent Kula

https://doi.org/10.32323/ujma.434361

Cited By: 4

Abstract

In this work, we give two methods to generate general helices that lie on the sphere  $S^{2n}$ in Euclidean (2n+1)-space $E^{2n+1}$.

Keywords

General helix, sphere, spherical curve

References

• [1] Ali, Ahmad T., Turgut, M.: Some characterizations of slant helices in the Euclidean space En, Hacettepe Journal of Mathematics and Statistics, 39, 327-336, (2010).
• [2] Breuer, S. and Gottlieb, D.: Explicit characterization of spherical curves, Proc. Am. Math. Soc., 274, 126–127, (1972).
• [3] Camci, C. Ilarslan, K. Kula, L. and Hacisalihoglu, H.H.: Harmonic cuvature and general helices, Chaos Solitons & Fractals, 40, 2590-2596, (2009).
• [4] Gluck, H.: Higher curvatures of curves in Euclidean space, Amer. Math. Monthly 73, 699-704, (1966).
• [5] Hayden, H. A.: On a general helix in a Riemannian n-space, Proc. London Math. Soc. 2, 37-45, (1931).
• [6] Monterde, J.,: Curves with constant curvature ratios, Bol. Soc. Mat. Mexicana 3a, 13/1, 177–186, (2007).
• [7] Romero-Fuster, M.C., Sanabria-Codesal, E.: Generalized helices, twistings and flattenings of curves in n-space. Mat. Cont., 17 , 267-280, (1999).
• [8] Struik, D.J.: Lectures on Classical Differential Geometry, Dover, New-York, (1988).
• [9] Wong Y.C.,: A global formulation of the condition for a curve to lie in a sphere, Monatsch Math, 67, 363–365, (1963).
• [10] Wong Y.C.,: On a explicit characterization of spherical curves, Proc. Am. Math. Soc., 34, 239–242, (1972).