2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68129We derive a correspondence between (Lorentzian) harmonic maps into the pseudosphere $S_1^2$, with appropriate regularity conditions, and certain connection 1-forms. To these harmonic maps, we associate a representation of type Weierstrass, and we apply it to construct timelike surfaces with constant mean curvature.Differential GeometryMathematical PhysicsMathematics Subject Classification: 53A10, 58E20text