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arXiv · 2109.13747

On polyharmonic helices in space forms

Volker Branding
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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.

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Volker Branding. 2023-01-25. On polyharmonic helices in space forms. https://doi.org/10.1007/s00013-022-01809-y

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