Osculating Mate of a Curve in Minkowski 3-Space

Öztürk İ., Çakır H., Özdemir M.

Axioms, cilt.14, sa.6, ss.1-26, 2025 (SCI-Expanded)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 6
  • Basım Tarihi: 2025
  • Doi Numarası: 10.3390/axioms14060468
  • Dergi Adı: Axioms
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
  • Sayfa Sayıları: ss.1-26
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

In this paper, we introduce and develop the concept of osculating curve pairs in the three-dimensional Minkowski space. By defining a vector lying in the intersection of osculating planes of two non-lightlike curves, we characterize osculating mates based on their Frenet frames. We then derive the transformation matrix between these frames and investigate the curvature and torsion relations under varying causal characterizations of the curves—timelike and spacelike. Furthermore, we determine the conditions under which these generalized osculating pairs reduce to well-known curve pairs such as Bertrand, Mannheim, and Bäcklund pairs. Our results extend existing theories by unifying several known curve pair classifications under a single geometric framework in Lorentzian space.