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