no. G11
Article de recherche - Géométrie et Topologie
Classification results for polyharmonic helices in space forms
[Résultats de classification des hélices polyharmoniques dans les espaces formes]
Branding, Volker1
1University of Vienna, Faculty of Mathematics Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
Comptes Rendus. Mathématique, Tome 362 (2024) no. G11, pp. 1521-1537

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.

Nous obtenons divers résultats de classification des hélices polyharmoniques, c’est à dire des courbes polyharmoniques dont les courbures géodésiques sont toutes constantes, dans les espaces formes. Nous obtenons une classification complète des hélices triharmoniques sur les sphères de dimension arbitraire. De plus, nous montrons que les hélices polyharmoniques d’ordre arbitraire à courbure géodésique non nulle dans des espaces formes de courbure négative sont des géodésiques.

Reçu le :
Révisé le :
Accepté le :
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DOI : 10.5802/crmath.666
Classification : 58E20, 53C43, 31B30, 58E10
Keywords: r-harmonic curves, helices, space form
Mots-clés : Courbes r-harmonique, hélices, espaces formes

Branding, Volker  1

1 University of Vienna, Faculty of Mathematics Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Classification results for polyharmonic helices in space forms},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1521--1537},
     year = {2024},
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Branding, Volker. Classification results for polyharmonic helices in space forms. Comptes Rendus. Mathématique, Tome 362 (2024) no. G11, pp. 1521-1537. doi: 10.5802/crmath.666

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