The Weyl functional on 4-manifolds of positive Yamabe invariant

Abstract

It is shown that on every closed oriented Riemannian 4-manifold (M, g) with positive scalar curvature,where W + g , χ(M ) and τ (M ) respectively denote the self-dual Weyl tensor of g, the Euler characteristic and the signature of M . This generalizes Gursky's inequality [15] for the case of b 1 (M ) > 0 in a much simpler way.We also extend all such lower bounds of the Weyl functional to 4-orbifolds including Gursky's inequalities for the case of b + 2 (M ) > 0 or δ g W + g = 0, and obtain topological obstructions to the existence of self-dual orbifold metrics of positive scalar curvature.