In this paper, we present a comprehensive study on the differential geometry of parallel curves derived from a tripartite family of pedal curves, specifically the tangent (T-pedal), principal normal (N-pedal), and binormal (B-pedal) tracks of a given regular space curve in Euclidean 3-space $ {E^3} $. By utilizing the classical moving Frenet-Serret frame, we explicitly derive the parametric equations of the parallel curves constructed from each spatial pedal family. Furthermore, the complete Frenet-Serret apparatus, including the localized moving trihedrons, curvature $ \kappa $, and torsion $ \tau $ functions of these parallel curves obtained from pedal curves of a given curve by using Frenet vectors as position vectors, were systematically determined.
Citation: Filiz Ertem Kaya. Differential geometry of parallel curves derived from pedal curves of a given curve in Euclidean 3-space[J]. AIMS Mathematics, 2026, 11(8): 24397-24418. doi: 10.3934/math.2026985
In this paper, we present a comprehensive study on the differential geometry of parallel curves derived from a tripartite family of pedal curves, specifically the tangent (T-pedal), principal normal (N-pedal), and binormal (B-pedal) tracks of a given regular space curve in Euclidean 3-space $ {E^3} $. By utilizing the classical moving Frenet-Serret frame, we explicitly derive the parametric equations of the parallel curves constructed from each spatial pedal family. Furthermore, the complete Frenet-Serret apparatus, including the localized moving trihedrons, curvature $ \kappa $, and torsion $ \tau $ functions of these parallel curves obtained from pedal curves of a given curve by using Frenet vectors as position vectors, were systematically determined.
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Filiz Ertem Kaya. Differential geometry of parallel curves derived from pedal curves of a given curve in Euclidean 3-space[J]. AIMS Mathematics, 2026, 11(8): 24397-24418. doi: 10.3934/math.2026985
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