The DPW method for constant mean curvature surfaces in 3-dimensional Lorentzian spaceforms, with applications to Smyth type surfaces

Abstract

We give criteria for singularities of spacelike constant mean curvature surfaces in 3-dimensional de Sitter and anti-de Sitter spaces constructed by the DPW method, which is a generalized Weierstrass representation. We also construct some examples of spacelike CMC surfaces, including analogs of Smyth surfaces with singularities, using appropriate models to visualize them.