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