On polyharmonic helices in space forms

Abstract

In this article we study polyharmonic curves of constant curvature where we mostly focus on the case of curves on the sphere. We classify polyharmonic curves of constant curvature in three-dimensional space forms and derive an explicit family of polyharmonic curves on the sphere. Our results give new insights into the geometric structure of higher order variational problems.

References in corpus (3)

• Polyharmonic hypersurfaces into pseudo-Riemannian space forms
• Unique continuation properties for polyharmonic maps between Riemannian manifolds
• On finite energy solutions of 4-harmonic and ES-4-harmonic maps

Cited by in corpus (3)

• On the normal stability of triharmonic hypersurfaces in space forms
• On the normal stability of the 4-harmonic and the ES-4-harmonic hypersphere
• Classification results for polyharmonic helices in space forms