Kirchhoff elastic rods in higher-dimensional space forms

Kirchhoff elastic rods in higher-dimensional space forms

In this paper, we give examples of Kirchhoff rod centerlines fully immersed in higher-dimensional space forms. More precisely, we prove that any helix in a space form is a Kirchhoff rod centerline. These examples imply the difference of the geometric properties between Kirchhoff rod centerlines and...

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Veröffentlicht in:Proceedings of the Japan Academy. Series A. Mathematical sciences 2011-01, Vol.87 (1), p.5-9
1. Verfasser: Kawakubo, Satoshi
Format: Artikel
Sprache:eng
Schlagworte:
58E10
74K10
Elastica
helix
Kirchhoff elastic rod
variational problem
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Zusammenfassung:In this paper, we give examples of Kirchhoff rod centerlines fully immersed in higher-dimensional space forms. More precisely, we prove that any helix in a space form is a Kirchhoff rod centerline. These examples imply the difference of the geometric properties between Kirchhoff rod centerlines and elasticae.
ISSN:0386-2194
DOI:10.3792/pjaa.87.5