Classification results for polyharmonic helices in space forms
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 ar...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.666/ |
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| _version_ | 1825206152188657664 |
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| author | Branding, Volker |
| author_facet | Branding, Volker |
| author_sort | Branding, Volker |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-589b960d37c54fc38c30af6756fcb646 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-589b960d37c54fc38c30af6756fcb6462025-02-07T11:23:50ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G111521153710.5802/crmath.66610.5802/crmath.666Classification results for polyharmonic helices in space formsBranding, Volker0University of Vienna, Faculty of Mathematics Oskar-Morgenstern-Platz 1, 1090 Vienna, AustriaWe 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.666/r-harmonic curveshelicesspace form |
| spellingShingle | Branding, Volker Classification results for polyharmonic helices in space forms Comptes Rendus. Mathématique r-harmonic curves helices space form |
| title | Classification results for polyharmonic helices in space forms |
| title_full | Classification results for polyharmonic helices in space forms |
| title_fullStr | Classification results for polyharmonic helices in space forms |
| title_full_unstemmed | Classification results for polyharmonic helices in space forms |
| title_short | Classification results for polyharmonic helices in space forms |
| title_sort | classification results for polyharmonic helices in space forms |
| topic | r-harmonic curves helices space form |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.666/ |
| work_keys_str_mv | AT brandingvolker classificationresultsforpolyharmonichelicesinspaceforms |