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January 2011 Kirchhoff elastic rods in higher-dimensional space forms
Satoshi Kawakubo
Proc. Japan Acad. Ser. A Math. Sci. 87(1): 5-9 (January 2011). DOI: 10.3792/pjaa.87.5

Abstract

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.

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Satoshi Kawakubo. "Kirchhoff elastic rods in higher-dimensional space forms." Proc. Japan Acad. Ser. A Math. Sci. 87 (1) 5 - 9, January 2011. https://doi.org/10.3792/pjaa.87.5

Information

Published: January 2011
First available in Project Euclid: 28 December 2010

zbMATH: 05906822
MathSciNet: MR2777230
Digital Object Identifier: 10.3792/pjaa.87.5

Subjects:
Primary: 58E10
Secondary: 74K10

Keywords: elastica , helix , Kirchhoff elastic rod , variational problem

Rights: Copyright © 2011 The Japan Academy

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Vol.87 • No. 1 • January 2011
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