Prescribed curvature tensor in locally conformally flat manifolds

Abstract

Our principal goal is to study the Prescribed Curvature Tensor problem in locally conformally flat manifolds. The solution to this problem is given explicitly for the special cases of the tensor R, including a case where the metric g is complete on Rn. Similar problems are considered for locally conformally flat manifolds. As applications of these results we exhibit explicit examples of metrics g, conformal to g they are solutions for this problem.

arXiv commentOur principal goal is to study the Prescribed Curvature Tensor problem in locally conformally flat manifolds