Prescribed Ricci curvature problem

Short description: Riemannian geometry mathematical problem

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

• Aubin, Thierry (1998) (in en). Some Nonlinear Problems in Riemannian Geometry. Springer Monographs in Mathematics. Springer Nature. doi:10.1007/978-3-662-13006-3. ISBN 9783540607526. 
• Besse, Arthur (2008) (in en). Einstein manifolds. Classics in Mathematics (Reprint of the 1987 ed.). Berlin: Springer. xii+516 pp.. ISBN 9783540152798. 
• DeTurck, Dennis M. (1981). "Existence of metrics with prescribed Ricci curvature: local theory". Inventiones Mathematicae 65 (1): 179–207. doi:10.1007/BF01389010. Bibcode: 1981InMat..65..179D.