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Coupled equations for Kähler metrics and Yang-Mills connections

Presented by: 
L Alvarez-Consul ICMAT
Tuesday 14th June 2011 - 10:00 to 11:00
INI Seminar Room 1
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]).
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons