Constructing $k$-Slant Curves in Three Dimensional Euclidean Spaces

Çetin Camcı

doi:10.53570/jnt.1647509

EN

Constructing $k$-Slant Curves in Three Dimensional Euclidean Spaces

Abstract

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 $k\geq 2$ in three dimensional Euclidean spaces. Furthermore, the position vector of a $k$-slant curve for a positive integer $k\geq 2$ has not been known thus far. In this paper, we propose a method for constructing $k$-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 $k \in \mathbb{N}$, 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 $k$-slant curves to magnetic curves. Finally, we discuss the need for further research.

Keywords

General helices, spherical curves, slant curves

References

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Details

Primary Language

English

Subjects

Algebraic and Differential Geometry

Journal Section

Research Article

Authors

Çetin Camcı ^*
0000-0002-0122-559X
Türkiye

Publication Date

March 28, 2025

Submission Date

February 26, 2025

Acceptance Date

March 27, 2025

Published in Issue

Year 2025 Number: 50

DOI

https://doi.org/10.53570/jnt.1647509

IZ

https://izlik.org/JA32SR82GA

APA

Camcı, Ç. (2025). Constructing $k$-Slant Curves in Three Dimensional Euclidean Spaces. Journal of New Theory, 50, 98-115. https://doi.org/10.53570/jnt.1647509

AMA

1.Camcı Ç. Constructing $k$-Slant Curves in Three Dimensional Euclidean Spaces. JNT. 2025;(50):98-115. doi:10.53570/jnt.1647509

Chicago

Camcı, Çetin. 2025. “Constructing $k$-Slant Curves in Three Dimensional Euclidean Spaces”. Journal of New Theory, nos. 50: 98-115. https://doi.org/10.53570/jnt.1647509.

EndNote

Camcı Ç (March 1, 2025) Constructing $k$-Slant Curves in Three Dimensional Euclidean Spaces. Journal of New Theory 50 98–115.

IEEE

[1]Ç. Camcı, “Constructing $k$-Slant Curves in Three Dimensional Euclidean Spaces”, JNT, no. 50, pp. 98–115, Mar. 2025, doi: 10.53570/jnt.1647509.

ISNAD

Camcı, Çetin. “Constructing $k$-Slant Curves in Three Dimensional Euclidean Spaces”. Journal of New Theory. 50 (March 1, 2025): 98-115. https://doi.org/10.53570/jnt.1647509.

JAMA

1.Camcı Ç. Constructing $k$-Slant Curves in Three Dimensional Euclidean Spaces. JNT. 2025;:98–115.

MLA

Camcı, Çetin. “Constructing $k$-Slant Curves in Three Dimensional Euclidean Spaces”. Journal of New Theory, no. 50, Mar. 2025, pp. 98-115, doi:10.53570/jnt.1647509.

Vancouver

1.Çetin Camcı. Constructing $k$-Slant Curves in Three Dimensional Euclidean Spaces. JNT. 2025 Mar. 1;(50):98-115. doi:10.53570/jnt.1647509