The main aim of this paper is to investigate the existence of Frenet helices which are polyharmonic of order r, shortly, r-harmonic. We shall obtain existence, non-existence and classification results. More specifically, we obtain a complete classification of proper r-harmonic helices into the $3$-dimensional solvable Lie group Sol₃. Next, we investigate the existence of proper r-harmonic helices into Bianchi-Cartan-Vranceanu spaces and, in this context, we find new examples. Finally, we shall establish some non-existence results both for Frenet curves and Frenet helices of order n ≥ 4 when the ambient space is the Euclidean sphere ᵐ.
No takes yet. Share an insight, caveat, or question.
Montaldo et al. (2024) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: