Prescribed curvature tensor in locally conformally flat manifolds

A global existence theorem for the prescribed curvature tensor problem in locally conformally flat manifolds is proved for a special class of tensors R. Necessary and sufficient conditions for the existence of a metric ḡ, conformal to Euclidean g, are determined such that R̄=R, where R̄ is the Riemannian curvature tensor of the metric ḡ. The solution to this problem is given explicitly for special cases of the tensor R, including the case where the metric ḡ is complete on Rn. Similar problems are considered for locally conformally flat manifolds.