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). 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). 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. Bibcode:1981InMat..65..179D. doi:10.1007/BF01389010.

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