Extremal Kaehler metrics on projective bundles over a curve - II

Vestislav Apostolov (Montréal)

I will discuss the existence of extremal Kaehler metrics (in the sense of Calabi) of non-constant scalar curvature on the total space of a projecteve bundle P(E) over a  compact complex curve. The problem is not solved in full generality even in the case of a projective plane bundle over CP^e1. However, I will show that sufficiently "small''  Kaehler classes admit extremal Kaehler metrics if and only if the underlying vector bundle E  can be decomposed as a sum of stable factors. The talk will be a sequel to P. Gauduchon's and is based on a recent work with D. Calderbak, P. Gauduchon and C. Tonnesen-Friedman.