Construction of Pedal Curves Using Different Types of Bishop Frames in Euclidean 3-Space

Öz

In this study, pedal curves defined by the Type-1, Type-2, and Type-3 Bishop frame vectors of a regular space curve in Euclidean 3-space are investigated. In addition, the pedal curves obtained from the unit Darboux vectors of the Bishop frames are also considered. The Frenet and Bishop frame vectors of these curves are determined, and their curvature and torsion functions are expressed in terms of the geometric invariants of the base curve. Furthermore, several examples are given, and the corresponding pedal curves are illustrated to present their geometric properties. The resulting curves form a new family of curves defined by the given frame structures in Euclidean 3-space.

Anahtar Kelimeler

• Pedal curves
• Bishop frame
• Darboux vector
• Frenet frame
• Curvature
• Torsion

Etik Beyan

Ethics committee approval was not required for this study because of there was no study on animals or humans.

Teşekkür

This study is based on the master’s thesis of the second author.

Kaynakça

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