Classification results for polyharmonic helices in space forms
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909392929030144 |
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| author | Branding, Volker |
| author_facet | Branding, Volker |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_04446 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Classification results for polyharmonic helices in space forms Branding, Volker Differential Geometry 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. |
| title | Classification results for polyharmonic helices in space forms |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2306.04446 |