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

References

  • {{cite book |last=Aubin |first=Thierry |author-link=Thierry Aubin |url= |title=Some Nonlinear Problems in Riemannian Geometry |publisher=Springer Nature |isbn=9783540607526 |series=Springer Monographs in Mathematics |location= |publication-date=1998 |language=en |doi=10.1007/978-3-662-13006-3}}
  • {{cite book |last=Besse |first=Arthur |author-link=Arthur Besse |url= |title=Einstein manifolds |publisher=Springer |isbn=9783540152798 |series=Classics in Mathematics |edition=Reprint of the 1987 |publication-place=Berlin |publication-date=2008 |at=xii+516 pp. |language=en |doi=}}
  • {{cite journal |last=DeTurck |first=Dennis M. |author-link=Dennis DeTurck |date=1981 |title=Existence of metrics with prescribed Ricci curvature: local theory |journal=Inventiones Mathematicae |volume=65 |issue=1 |pages=179–207|doi=10.1007/BF01389010 |bibcode=1981InMat..65..179D }}

Category:Riemannian geometry

Category:Mathematical problems

ricci curvature

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