Akademik Veri Yönetim Sistemi
International Symposium on Differential Geometry and Applications, Tunceli, Türkiye, 3 - 04 Temmuz 2025, ss.116-117, (Özet Bildiri)
This study introduces and investigates osculating curve pairs in the three-dimensional Minkowski space as a generalization of known associated curves. These pairs are defined via a shared unit vector that lies in the intersection of the osculating planes of two non-lightlike curves and makes a fixed angle with their tangent vectors. The classification is performed based on the causal character of the curves, and transformation matrices between the respective Frenet frames are derived. Curvature and torsion relations are obtained for various configurations, and conditions under which the osculating pairs reduce to Bertrand, Mannheim, or Bäcklund pairs are examined. The results provide a geometric framework that unifies several classical curve pair types in the context of Lorentzian geometry.