Persistent Lorentzian Rigid Motions Generated by Slant Helices in Minkowski 3-Space
Mathematics, cilt.14, sa.13, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 14 Sayı: 13
- Basım Tarihi: 2026
- Doi Numarası: 10.3390/math14132415
- Dergi Adı: Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, zbMATH, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: Frenet–Serret frame, Lorentzian geometry, Minkowski space, persistent rigid motions, rigid-body kinematics, slant helices
- Ankara Üniversitesi Adresli: Evet
Özet
This paper develops a unified Lorentzian framework for persistent rigid motions generated by slant helices in three-dimensional Minkowski space and investigates their geometric and kinematic properties. Persistence is characterized by the constancy of the pitch of the instantaneous twist associated with a one-parameter rigid motion in the Poincaré group (Formula presented.). Interpreting curves in the motion group as trajectories of rigid motions, we study Frenet–Serret and adapted frame motions determined by slant helices under different causal characters. Necessary and sufficient conditions are established for these frame motions to generate persistent Lorentzian motions. An explicit intrinsic relationship between the pitches of Frenet–Serret and adapted frame motions is obtained in terms of the geodesic curvature of the spherical image of the principal normal indicatrix, showing that persistence is governed by intrinsic curve invariants and is independent of the chosen moving frame. The geometric structure of persistent motions is further clarified through associated ruled surfaces. In particular, the pitch of a persistent motion is shown to coincide with the distribution parameter of the ruled surface associated with the corresponding frame motion. Illustrative examples are presented for different causal configurations. These results extend classical Euclidean theory of persistent rigid motions to the Lorentzian setting and provide a unified framework connecting curve theory, frame geometry, ruled surfaces, and Lorentzian kinematics.