Harmonic 2-forms and positively curved 4-manifolds

Abstract

We prove that if a compact Riemannian 4-manifold with positive sectional curvature satisfies a Kato type inequality, then it is definite. We also discuss some new insights for compact Riemannian 4-manifolds of positive sectional curvature.

We remark that the results in this paper were obtained in 2012. While trying to derive more complete result from the formulas in this paper, we have circulated this paper among many colleagues for the past several years