Editing Ricci flow (section)

===Possible extensions===
Given any {{mvar|n}} larger than two, there exist many closed {{mvar|n}}-dimensional smooth manifolds which do not have any smooth Riemannian metrics of constant curvature. So one cannot hope to be able to simply drop the curvature conditions from the above convergence theorems. It could be possible to replace the curvature conditions by some alternatives, but the existence of compact manifolds such as [[complex projective space]], which has a metric of nonnegative curvature operator (the [[Fubini-Study metric]]) but no metric of constant curvature, makes it unclear how much these conditions could be pushed. Likewise, the possibility of formulating analogous convergence results for negatively curved Riemannian metrics is complicated by the existence of closed Riemannian manifolds whose curvature is arbitrarily close to constant and yet admit no metrics of constant curvature.<ref>{{cite journal |last1=Gromov |first1=M. |last2=Thurston |first2=W. |title=Pinching constants for hyperbolic manifolds |journal=Invent. Math. |date=1987 |volume=89|issue=1 |pages=1–12|doi=10.1007/BF01404671|bibcode=1987InMat..89....1G |s2cid=119850633 }}</ref>