A characterization of rotational minimal surfaces in the de Sitter space

TL;DR

This paper characterizes the generating curves of rotational minimal surfaces in de Sitter space as solutions to a variational problem, extending classical Euclidean results to a Lorentzian setting.

Contribution

It introduces a variational characterization of these curves, linking them to the critical points of the center of mass with fixed endpoints and length.

Findings

Curves are critical points of the center of mass functional.

Extension of Euclidean catenary and catenoid properties to de Sitter space.

Provides a new variational perspective on minimal surfaces in Lorentzian geometry.

Abstract

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.