Polyharmonic helices

2024/04/21 by Montaldo, Stefano, Ratto, Andrea · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.13726

Abstract

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 \s^m.

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• Polyharmonic curves in semi-Riemannian manifolds

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