%0 Journal Article
%A Muñoz Masqué, Jaime
%A Pozo Coronado, Luis Miguel
%A Sánchez Rodríguez, I.
%T The prescribed curvature problem in dimension four.
%D 2009
%@ 0021-7824
%U https://hdl.handle.net/20.500.14352/50239
%X Necessary 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.
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