Coupled equations for Kähler metrics and Yang-Mills connections
Seminar Room 1, Newton Institute
We study equations on a principal bundle over a compact complex manifold coupling a connection on the bundle with a Kähler structure on the base. These equations generalize the conditions of constant scalar curvature for a Kähler metric and Hermite-Yang-Mills for a connection. We provide a moment map interpretation of the equations and study obstructions for the existence of solutions, generalizing the Futaki invariant, the Mabuchi K-energy and geodesic stability. We finish by giving some examples of solutions. This is joint work with Mario Garcia-Fernandez and Oscar Garcia-Prada (arXiv:1102.0991 [math.DG]).