THE GEOMETRY OF THE MODULI SPACE OF CP2 INSTANTONS

The moduli space ℳ of self-dual connections ("instantons") of instanton number k=1 over CP2 is topologically a cone on CP2. The complement ℳ* of the vertex of this cone carries a natural Riemannian metric (the "L2 metric"). We find an explicit formula for this metric and deduce certain consequences. In particular, (i) the boundary ∂ℳ is a totally geodesic submanifold of the completion, (ii) ℳ is positively curved at ∂ℳ, and (iii) ℳ is negatively curved in certain directions near the vertex of the cone. © 1990 Springer-Verlag.