Alvarez-Consul, LuisGarcia-Fernandez, MarioGarcia-Prada, Oscar2014-01-092014-01-092014-01-09201310.2140/gt.2013.17.2731https://infoscience.epfl.ch/handle/20.500.14299/99113WOS:000327541500005We 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.text::journal::journal article::research article