Dual quaternions and dual quaternionic curves
Copyright policy )Dual quaternions and dual quaternionic curves
After a brief review of the different types of quaternions, we develop a new perspective for dual quaternions with dividing two parts. Due to this new perspective, we will define the isotropic and nonisotropic dual quaternions. Then we will also give the basic algebraic concepts about the dual quaternions. Moreover, we define isotropic dual quaternionic curves and non-isotropic dual quaternionic curves. Via these definitions we find Serret-Frenet formulae for isotropic dual quaternionic curves. Finally, we will use these results to derive the Serret-Frenet formulae for non-isotropic dual quaternionic curves.
- Yıldız Technical University Turkey
Classical differential geometry, Serret-Frenet frame, Non-Euclidean differential geometry, Quaternion and other division algebras: arithmetic, zeta functions, dual quaternionic curves, dual quaternions
Classical differential geometry, Serret-Frenet frame, Non-Euclidean differential geometry, Quaternion and other division algebras: arithmetic, zeta functions, dual quaternionic curves, dual quaternions
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