Muñoz Masqué, JaimePozo Coronado, Luis MiguelSánchez Rodríguez, I.2023-06-202023-06-2020090021-782410.1016/j.matpur.2009.10.003https://hdl.handle.net/20.500.14352/50239Necessary and sufficient conditions for a g-valued differential 2-form on a 4-dimensional manifold to be, locally, a curvature; form, are given. The dimension four is exceptional for the problem of prescribed curvature as, in this dimension, Bianchi's identities can be eliminated for a large class of Lie algebras, including semisimple algebras. Hence, the curvature forms are characterized as the solutions to a second-order partial differential system, which is proved to be formally integrable.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0021782409001317http://www.sciencedirect.comrestricted access514515.1Bianchi identityCurvature formFormal integrabilityLie algebraGeometríaTopología1204 Geometría1210 Topología