Prescribed curvature tensor in locally conformally flat manifolds

A global existence theorem for the prescribed curvature tensor problem in locally con formally flat manifolds is proved for a special class of tensors R. Necessary and sufficient conditions for the existence of a metric (g) over bar, conformal to Euclidean g, are determined such that (R) over bar = R, where (R) over bar is the Riemannian curvature tensor of the metric (g) over bar. The solution to this problem is given explicitly for special cases of the tensor R, including the case where the metric (g) over bar is complete on R-n. Similar problems are considered for locally conformally flat manifolds. (C) 2017 Elsevier B.V. All rights reserved.