Kenmotsu-Bryant type representation formula for constant mean curvature spacelike surfaces in \({\mathbf H}_1^3(-c^2)\) (Q1295471)

The main purpose of this paper is to give a representation formula for constant mean curvature (CMC) spacelike surfaces (including maximal surfaces) in anti-de Sitter \(3\)-space \(\text{Ad }S\) of constant negative curvature \(-c^2\), similar to the Kenmotsu type representation formula for nonzero constant mean curvature spacelike surfaces in Minkowski \(3\)-space \(\mathbb{L}^3\). This formula is given as an explicit integrable differential equation of first order for an immersed CMC spacelike surface \(M\) in \(\text{Ad }S\), by means of a given harmonic map from \(M\) to the hyperbolic 2-plane \(\mathbb{H}^2\).