Classification results for polyharmonic helices in space forms

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Abstract

We derive various classification results for polyharmonic helices, which are polyharmonic curves whose geodesic curvatures are all constant, in space forms. We obtain a complete classification of triharmonic helices in spheres of arbitrary dimension. Moreover, we show that polyharmonic helices of arbitrary order with non-zero geodesic curvatures to space forms of negative curvature must be geodesics.

Original languageEnglish
Pages (from-to)1521-1537
Number of pages17
JournalComptes Rendus Mathematique
Volume362
DOIs
Publication statusPublished - 2024

Austrian Fields of Science 2012

  • 101006 Differential geometry

Keywords

  • helices
  • r-harmonic curves
  • space form

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