English

Classification results for polyharmonic helices in space forms

Differential Geometry 2024-11-19 v2

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-vanishing geodesic curvatures to space forms of negative curvature must be geodesics.

Keywords

Cite

@article{arxiv.2306.04446,
  title  = {Classification results for polyharmonic helices in space forms},
  author = {Volker Branding},
  journal= {arXiv preprint arXiv:2306.04446},
  year   = {2024}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2109.13747

R2 v1 2026-06-28T10:58:52.468Z