A Characterization of Minimal Rotational Surfaces in the de Sitter Space

In this paper, it is characterized the generating curves of minimal rotational surfaces in the de Sitter space S 1 3 as solutions of a variational problem. More exactly, it is proved that these curves are the critical points of a potential energy functional involving the distance to a given plane among all curves of S 1 2 with prescribed endpoints and fixed length. This extends the known Euler’s result that asserts that the catenary is the generating curve of the catenoid.