Scalar curvature and connected sums of self-dual 4-manifolds
Under a reasonable vanishing hypothesis, Donaldson and Friedman proved that the connected sum of two self-dual Riemannian 4-manifolds is again self-dual. Here we prove that the same result can be extended to the positive scalar curvature case. This is an analogue of the classical theorem of Gromov–Lawson and Schoen–Yau in the self-dual category. The proof is based on twistor theory.