Editing Complex projective plane (section)

==Differential geometry==
As a [[Riemannian manifold]], the complex projective plane is a 4-dimensional manifold whose sectional curvature is quarter-pinched, but not strictly so. That is, it attains ''both'' bounds and thus evades being a sphere, as the [[sphere theorem]] would otherwise require.  The rival normalisations are for the curvature to be pinched between 1/4 and 1; alternatively, between 1 and 4.  With respect to the former normalisation, the imbedded surface defined by the complex projective line has [[Gaussian curvature]] 1.  With respect to the latter normalisation, the imbedded real projective plane has Gaussian curvature 1.

An explicit demonstration of the Riemann and Ricci tensors is given in the ''n''=2 subsection of the article on the [[Fubini-Study metric]].