Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on polyharmonic curves of constant curvature   In this article we study \(r\)-harmonic curves of constant curvature where we
mostly focus on the case of curves on the sphere. By performing various
explicit calculations for \(r=2,3,4\) we deduce various insights on the
structure of such curves. Building on these results we classify \(r\)-harmonic
curves of constant curvature in three-dimensional space forms and derive an
explicit family of \(r\)-harmonic curves on the sphere. To establish our main
results we combine a variety of techniques for one-dimensional variational
problems.

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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci