## Tohoku Mathematical Journal

### Kirchhoff elastic rods in a Riemannian manifold

Satoshi Kawakubo

#### Abstract

Imagine a thin elastic rod like a piano wire. We consider the situation that the elastic rod is bent and twisted and both ends are welded together to form a smooth loop. Then, does there exist a stable equilibrium? In this paper, we generalize the energy of uniform symmetric Kirchhoff elastic rods in the $3$-dimensional Euclidean space to consider such a variational problem in a Riemannian manifold. We give the existence and regularity of minimizers of the energy in a compact or homogeneous Riemannian manifold.

#### Article information

Source
Tohoku Math. J. (2), Volume 54, Number 2 (2002), 179-193.

Dates
First available in Project Euclid: 11 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1113247562

Digital Object Identifier
doi:10.2748/tmj/1113247562

Mathematical Reviews number (MathSciNet)
MR1904948

Zentralblatt MATH identifier
1011.58008

#### Citation

Kawakubo, Satoshi. Kirchhoff elastic rods in a Riemannian manifold. Tohoku Math. J. (2) 54 (2002), no. 2, 179--193. doi:10.2748/tmj/1113247562. https://projecteuclid.org/euclid.tmj/1113247562

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