Torsion-free Connections with prescribed Curvature

We provide necessary and sufficient conditions for a curvature map S U K(g) to arise from the curvature tensor of a torsion-free connection on a sufficiently small U'⊂ U by using a suitable power series approach. This torsion-free connection is uniquely given. The curvature map S is used to effectively compute the holonomy of this connection.