Spacelike constant mean curvature 1 trinoids in de Sitter three-space (Q854537)

Surfaces of constant mean curvature (CMC) in pseudo-Riemannian space forms have properties quite similar to CMC surfaces in Riemannian space forms. In particular, there exist representation theorems by null holomorphic maps for minimal surfaces in Euclidean \(3\)-space \(\mathbb E^3\), CMC \(1\) surfaces in hyperbolic \(3\)-space \(\mathbb H^3(-1)\), space-like maximal surfaces in Lorentzian \(3\)-space \(\mathbb L^3\) and space-like CMC \(1\) surfaces in de Sitter \(3\)-space \(\mathbb S^3_1(1)\), which enable the authors to use the powerful complex function theory for studying these surfaces. More precisely, in the present paper the authors develop a representation formula for CMC \(1\) space-like surfaces in \(\mathbb S^3_1(1)\) in terms of holomorphic spinors and use it to construct examples of space-like catenoids and trinoids with constant mean curvature \(1\).