Geodesic
Free elasticae and Willmore tori in warped product spaces
Glasgow mathematical journal, Tome 40 (1998) no. 2, pp. 265-272

Voir la notice de l'article provenant de la source Cambridge University Press

We use the principle of symmetric criticality to connect the Willmore variational problem for surfaces in a warped product space with base a circle, and the free elastica variational problem for curves on its fiber. In addition we obtain a rational oneparameter family of closed helices in the anti De Sitter 3-space which are critical points of the total squared curvature functional. This means they are free elasticae. Also they are spacelike; this allows us to construct a corresponding family of spacelike Willmore tori in a certain kind of spacetime close to the Robertson-Walker spaces. 
Barros, Manuel. Free elasticae and Willmore tori in warped product spaces. Glasgow mathematical journal, Tome 40 (1998) no. 2, pp. 265-272. doi: 10.1017/S0017089500032596
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