On polyharmonic helices in space forms

TL;DR

This paper classifies polyharmonic curves of constant curvature in space forms, especially on the sphere, providing explicit examples and advancing understanding of higher order variational problems in differential geometry.

Contribution

It offers a complete classification of polyharmonic curves of constant curvature in three-dimensional space forms and constructs explicit examples on the sphere.

Findings

Classification of polyharmonic curves in space forms

Explicit family of polyharmonic curves on the sphere

New insights into higher order variational problems

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.