The Riemannian geometry of the Yang-Mills moduli space

The moduli space M of self-dual connections over a Riemannian 4-manifold has a natural Riemannian metric, inherited from the L2 metric on the space of connections. We give a formula for the curvature of this metric in terms of the relevant Green operators. We then examine in great detail the moduli space M1 of k=1 instantons on the 4-sphere, and obtain an explicit formula for the metric in this case. In particular, we prove that M1 is rotationally symmetric and has ''finite geometry'': it is an incomplete 5-manifold with finite diameter and finite volume. (orig.)