2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136626Holomorphic principal G-bundles over a complex manifold M can be studied using non-abelian cohomology groups H^1(M,G). On the other hand, if M=Σis a closed Riemann surface, there is a correspondence between holomorphic principal G-bundles over Σand coadjoint orbits in the dual of a central extension of the Lie algebra C^\infty(Σ, \g). We review these results and provide the details of an integrability condition for almost complex structures on smoothly trivial bundles. This article is a shortened version of the author's Diplom thesis.17 pagesDifferential GeometryComplex Variables58D27; 81R10; 32Q60text