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 language | English |
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Pages (from-to) | 1521-1537 |
Number of pages | 17 |
Journal | Comptes Rendus Mathematique |
Volume | 362 |
DOIs | |
Publication status | Published - 2024 |
Austrian Fields of Science 2012
- 101006 Differential geometry
Keywords
- helices
- r-harmonic curves
- space form