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Journal article

Coupled equations for Kahler metrics and Yang-Mills connections

Alvarez-Consul, Luis; Garcia-Fernandez, Mario; Garcia-Prada, Oscar
  • Published in: Geometry & Topology (ISSN: 1465-3060), vol. 17, num. 5, p. 2731-2812
  • Coventry: Geometry & Topology Publications, 2013

We study equations on a principal bundle over a compact complex manifold coupling a connection on the bundle with a Kahler structure on the base. These equations generalize the conditions of constant scalar curvature for a Kahler 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.

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