Akademik Veri Yönetim Sistemi
Journal of New Theory, sa.50, ss.98-115, 2025 (Hakemli Dergi)
Helices and constant procession curves are special examples of slant curves. However, there is no example of a 𝑘-slant curve for a positive integer 𝑘 ≥ 2 in three dimensional Euclidean spaces. Furthermore, the position vector of a 𝑘-slant curve for a positive integer 𝑘 ≥ 2 has not been known thus far. In this paper, we propose a method for constructing 𝑘 k-slant curves in three dimensional Euclidean spaces. We then show that spherical 𝑘-slant curves and 𝑁 𝑘 -constant procession curves can be derived from circles, for 𝑘 ∈ 𝑁, the set of all nonnegative integers. In addition, we provide a new proof of the spherical curve characterization and define a curve in the sphere called a spherical prime curve. Afterward, we apply 𝑘 k-slant curves to magnetic curves. Finally, we discuss the need for further research.