HYPERSPHERICAL AND HYPERCYLINDRICAL GENERALIZED HELICES IN THE SENSE OF HAYDEN IN $\mathbb{E}^{2n+1}$

Abstract

In this paper, we investigate generalized helices in the sense of Hayden in $(2n+1)$-dimensional Euclidean space  $\mathbb{E}^{2n+1}$. We obtain some results for such curves in $\mathbb{E}^{2n+1}$.  Thereafter, we obtain two families of generalized helices which are hyperspherical and hypercylindrical generalized helices in the sense of Hayden. Later, we give examples of hyperspherical and hypercylindrical generalized helices in the sense of Hayden in $\mathbb{E}^{5}$. Finally, we give examples of hyperspherical and hypercylindrical generalized helices in the sense of Hayden in $\mathbb{E}^{3}$ and illustrated the graphics of these curves with Mathematica 10.0.