On a Study of the Quaternionic Lorentzian Curve

Öz

In this study, Serret-Frenet Formulas for a space-quaternionic curve were obtained by considering quaternions and pseudo-quaternions in three-dimensional Lorentz Space . The Serret-Frenet Formulas for a Quaternionic Lorentz Curve  were then re-derived using them. 

Anahtar Kelimeler

• Ruled surfaces,lightlike curves,lightlike surfaces,Minkowski space,distribution parameter,Laplacian and D’Alembertian operator

Kaynakça

1. 1. Bharathi K. and M. Nagaraj, “Geometry of Quaternionic and Pseudo-Quaternionic Multiplications”, Ind. J. P. App. Math., 16(7): 741-756, (1985).
2. 2. Bharathi K. and Nagaraj M., “Quaternion Valued Function of a Real Variable Serret-Frenet Formulae”, Ind. J. P. App. Math., 18(6): 507-511, (1987).
3. 3. Sivridag A. I., Gunes R. and Keles S., “The Serret-Frenet Formulae for Dual Quaternion Valued Functions of a Single Real Variable”, Mechanism and Machine Theory, 29(5): 749-754, (1994).
4. 4. M. Karadag, “Helixes and Characterisations on the Quaternionic Lorentz Manifolds”, Doctoral Dissertation, University of Inonu, (1999).