Abstract
In this paper, we define framed slant helices and give a necessary and sufficient condition for them in three-dimensional Euclidean space. Then, we introduce the spherical images of a framed curve. Also, we examine the relations between a framed slant helix and its spherical images. Moreover, we give an example of a framed slant helix and its spherical images with figures.
Highlights
1 Introduction Let γ be a regular curve with the Frenet apparatus {T, N, B, κ, τ } in three-dimensional Euclidean space R3
We know that the curve γ is a general helix if the tangent vector of γ makes a constant angle with a fixed straight line
The curve γ is a slant helix if its normal vector makes a constant angle with a fixed straight line
Summary
Let γ be a regular curve with the Frenet apparatus {T, N, B, κ, τ } in three-dimensional Euclidean space R3. Γ is a framed helix if and only if the following equation holds: q(s) = ∓ cot φ(s), p(s) where φ is a constant angle (see [11]). 3 Framed slant helices in R3 we define a framed slant helix and its axis in three-dimensional Euclidean space R3.
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