Compact Riemannian manifolds with positive curvature operators

Abstract

M is said to have positive curvature operators if the eigenvalues of Z are positive at each point p € M. Meyer used the theory of harmonic forms to prove that a compact oriented n-dimensional Riemannian manifold with positive curvature operators must have the real homology of an n-dimensional sphere [GM, Proposition 2.9]. Using the theory of minimal two-spheres, we will outline a proof of the following stronger result.