Classification results for polyharmonic helices in space forms

Volker Branding

doi:10.5802/crmath.666

Article de recherche - Géométrie et Topologie

Classification results for polyharmonic helices in space forms
[Résultats de classification des hélices polyharmoniques dans les espaces formes]

Volker Branding ¹

¹ University of Vienna, Faculty of Mathematics Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria

Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1521-1537.

Résumé
Abstract

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.

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.

Reçu le : 2024-01-10
Révisé le : 2024-04-19
Accepté le : 2024-07-09
Publié le : 2024-11-14

DOI : 10.5802/crmath.666

Classification : 58E20, 53C43, 31B30, 58E10
Keywords: r-harmonic curves, helices, space form
Mot clés : Courbes r-harmonique, hélices, espaces formes

Affiliations des auteurs :

Volker Branding 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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     author = {Volker Branding},
     title = {Classification results for polyharmonic helices in space forms},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1521--1537},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     year = {2024},
     doi = {10.5802/crmath.666},
     language = {en},
}

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Volker Branding. Classification results for polyharmonic helices in space forms. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1521-1537. doi : 10.5802/crmath.666. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.666/

Bibliographie
Cité par

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[3] Volker Branding On p-biharmonic curves, J. Math. Anal. Appl., Volume 538 (2024) no. 2, 128384 | DOI | MR | Zbl

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