On Associated Curves of a Framed Curve in Euclidean 4−space

Önder Gökmen Yıldız; Selin Kaynar

On Associated Curves of a Framed Curve in Euclidean 4−space

Abstract

In this paper, we define some new curves, called associated curves, for a singular curve in Euclidean $4-$space by using its framed frame. We give necessary and sufficient conditions for these associated curves to be helices. Furthermore, we introduce a new type of rectifying curve derived from the associated curve and give its characterization.

Keywords

Associated curve, Framed curves, General helices, Integral curve, Rectifying curve, Singular points, Slant helices

References

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Details

Primary Language

English

Subjects

Algebraic and Differential Geometry

Journal Section

Research Article

Authors

Önder Gökmen Yıldız ^*
0000-0002-2760-1223
Türkiye

Selin Kaynar
0009-0003-4916-927X
Türkiye

Early Pub Date

December 29, 2025

Publication Date

December 29, 2025

Submission Date

July 8, 2025

Acceptance Date

August 15, 2025

Published in Issue

Year 2025 Volume: 1 Number: 1

IZ

https://izlik.org/JA97WR42EH

APA

Yıldız, Ö. G., & Kaynar, S. (2025). On Associated Curves of a Framed Curve in Euclidean 4−space. Sakarya Journal of Mathematics, 1(1), 1-6. https://izlik.org/JA97WR42EH

AMA

1.Yıldız ÖG, Kaynar S. On Associated Curves of a Framed Curve in Euclidean 4−space. Sakarya Journal of Mathematics. 2025;1(1):1-6. https://izlik.org/JA97WR42EH

Chicago

Yıldız, Önder Gökmen, and Selin Kaynar. 2025. “On Associated Curves of a Framed Curve in Euclidean 4−space”. Sakarya Journal of Mathematics 1 (1): 1-6. https://izlik.org/JA97WR42EH.

EndNote

Yıldız ÖG, Kaynar S (December 1, 2025) On Associated Curves of a Framed Curve in Euclidean 4−space. Sakarya Journal of Mathematics 1 1 1–6.

IEEE

[1]Ö. G. Yıldız and S. Kaynar, “On Associated Curves of a Framed Curve in Euclidean 4−space”, Sakarya Journal of Mathematics, vol. 1, no. 1, pp. 1–6, Dec. 2025, [Online]. Available: https://izlik.org/JA97WR42EH

ISNAD

Yıldız, Önder Gökmen - Kaynar, Selin. “On Associated Curves of a Framed Curve in Euclidean 4−space”. Sakarya Journal of Mathematics 1/1 (December 1, 2025): 1-6. https://izlik.org/JA97WR42EH.

JAMA

1.Yıldız ÖG, Kaynar S. On Associated Curves of a Framed Curve in Euclidean 4−space. Sakarya Journal of Mathematics. 2025;1:1–6.

MLA

Yıldız, Önder Gökmen, and Selin Kaynar. “On Associated Curves of a Framed Curve in Euclidean 4−space”. Sakarya Journal of Mathematics, vol. 1, no. 1, Dec. 2025, pp. 1-6, https://izlik.org/JA97WR42EH.

Vancouver

1.Önder Gökmen Yıldız, Selin Kaynar. On Associated Curves of a Framed Curve in Euclidean 4−space. Sakarya Journal of Mathematics [Internet]. 2025 Dec. 1;1(1):1-6. Available from: https://izlik.org/JA97WR42EH