konuralp j. math.

Konuralp Journal of Mathematics

2147-625X

Mehmet Zeki SARIKAYA

Applied Mathematics (Other)

Uygulamalı Matematik (Diğer)

On Characterizations of Osculating Curves using Darboux Frame in Minkowski 3-Space

https://orcid.org/0000-0001-5273-7897

Eren

Kemal

Sakarya Üniversitesi Matematik Bölümü, Sakarya.Türkiye Carlı

Mahmutcan

ORDU UNIVERSITY

https://orcid.org/0000-0002-7183-7081

Ersoy

Soley

SAKARYA UNIVERSITY

04 30 2026

14 1 242 249 12 15 2025 04 01 2026

2013

Konuralp Journal of Mathematics

In this paper, we investigate osculating curves in Minkowski 3-space by means of the Darboux frame associated with a non-null curve lying on a surface. Moreover, we introduce and construct two distinct classes of osculating curves, namely type-1 and type-2 osculating curves. Using the Darboux frame, we derive necessary and sufficient conditions under which a non-null curve lying on a surface becomes an osculating curve, expressed in terms of the geodesic curvature ${k_g}$, normal curvature ${k_n}$, and geodesic torsion ${\tau _g}$. As a consequence of these conditions, several corollaries and theorems concerning type-1 and type-2 osculating curves are established. Finally, illustrative examples supporting the theoretical results are presented, and graphical visualizations of the obtained curves are provided to demonstrate their geometric behavior.

Darboux frame osculating curve geodesic torsion geodesic curvature normal curvature

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