On the Differential Geometry of Tq - Pedal, Nq - Pedal and Bq - Pedal Curves Derived Via Quasi-Frames in Euclidean 3-Space E^3

Öz

This paper investigates the differential geometric properties of generalized pedal curves in Euclidean 3-space , constructed using the Quasi-frame apparatus along a space curve α(s). By projecting the position vector onto the quasi-frame field , we define the pedal (tangent-quasi pedal), pedal (normal-quasi pedal), and pedal (binormal-quasi pedal) curves with respect to a given origin O. We establish the explicit derivative formulas, tangent vectors, arclength parameters, principal curvatures, and torsions for each associated pedal curve. Furthermore, we analyze the geometric conditions under which these pedal curves become degenerate, planar, or straight line and explore the relationships between their quasi-curvature functions and the original curve's geometry.

Anahtar Kelimeler

• Quasi-frame (q-frame)
• Tq-pedal curves
• nq-pedal curves
• Pedal curves
• Quasi-pedal curvature
• Quasi-pedal torsion

Proje Numarası

No project number

Etik Beyan

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

Kaynakça

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