Four-manifolds of pinched sectional curvature (Q2171869)

The paper is about the interesting topic of four-dimensional manifolds. The authors show that under various curvature pinching conditions (for example, the sectional curvature is no more than 5/6 of the smallest Ricci eigenvalue), the manifold is definite. If restricting to a metric with harmonic Weyl tensor, it must be self-dual or anti-self-dual under the same conditions. Similarly, if restricting to an Einstein metric, it must be either the complex projective space with its Fubini-Study metric, the round sphere, or the quotient of one of these. Furthermore, they classify Einstein manifolds with positive intersection form and an upper bound on the sectional curvature.