Prescribed Ricci curvature problem explained

In Riemannian geometry, a branch of mathematics, the prescribed Ricci curvature problem is as follows: given a smooth manifold M and a symmetric 2-tensor h, construct a metric on M whose Ricci curvature tensor equals h.

See also

• Prescribed scalar curvature problem

References

• Thierry Aubin, Some nonlinear problems in Riemannian geometry. Springer Monographs in Mathematics, 1998.
• Arthur L. Besse. Einstein manifolds. Reprint of the 1987 edition. Classics in Mathematics. Springer-Verlag, Berlin, 2008. xii+516 pp.
• Dennis M. DeTurck, Existence of metrics with prescribed Ricci curvature: local theory. Invent. Math. 65 (1981/82), no. 1, 179–207.