  The generating curves of rotational minimal surfaces in the de Sitter space
$\s_1^3$ are characterized as solutions of a variational problem. It is proved
that these curves are the critical points of the center of mass among all
curves of $\s_1^2$ with prescribed endpoints and fixed length. This extends the
known properties of the catenary and the catenoid in the Euclidean setting.

Differential Geometry