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 .

Slant Helices that Constructed from Hyperspherical Curves in the n-dimensional Euclidean Space

“…With straightforward computations, we have the spherical general helix α (See [4]) with…”

Generalized Bertrand and Mannheim Curves in 3D Lie Groups

“…Lancret gave the condition for a given curve to be a general helices by the ratio of its curvatures to be constant [1]. In [2], a different approach is given to a general helix lying on a sphere. Also, slant helix was defined as a curve whose normal vector makes a constant angle with a fixed straight line in 3D Euclidean space by Izumiya and Takeuchi [3].…”

Tubular surfaces associated with framed base curves in Euclidean 3‐space

“…These surfaces, where their analytical and geometric properties are also examined, have added a different perspective to surface theory in Euclidean or different spaces. [10][11][12][13][14][15][16] Our aim in this study is to investigate the geometric properties of a tubular surface associated with a framed base curve. Also, the characterizations of the parameter curves of the tubular surface are examined.…”

“…If the radius of the sphere forming the canal surface is constant, these canal surfaces are called the tubular surface. These surfaces, where their analytical and geometric properties are also examined, have added a different perspective to surface theory in Euclidean or different spaces 10–16 …”