2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68128The paper presents a generalized Weierstrass representation for pseudospherical surfaces in terms of 3x3 matrices, using moving frames and loop group decompositions. The construction of all such surfaces, starting from a given representation, constitutes the subject of a separate, ulterior report. The appendix of the present work gives an elementary proof of the Birkhoff decomposition theorem for "loop-groups" of spectral parameter based on the real line, instead of the unit circle.35 pagesDifferential GeometryAnalysis of PDEs53A10, 53C42, 58D10,49Q05text