A NOTE ON EXTREMAL METRICS OF NONCONSTANT SCALAR CURVATURE

By working in C(n) with potentials of the form a log u + s(u), u the square of the distant to the origin, we obtain extremal Kahler metrics of non-constant scalar curvature on the blow-up of C(n) at 0 over arrow pointing right. We then show that these metrics can be completed at infinity by adding a CP(n-1), and reobtain the extremal Kahler metrics of non-constant scalar curvature constructed by Calabi on the blow-up of CP(n) at one point. A similar construction produces this type of metrics on other bundles over CP(n-1).