Prescribed Ricci curvature 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

Thierry Aubin, Some nonlinear problems in Riemannian geometry. Springer Monographs in Mathematics, 1998.
Dennis M. DeTurck, Existence of metrics with prescribed Ricci curvature: local theory. Invent. Math. 65 (1981/82), no. 1, 179–207.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.