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arXiv · 1102.0991

Coupled equations for Kähler metrics and Yang-Mills connections

Luis Alvarez-Consul·Mario Garcia-Fernandez·Oscar Garcia-Prada
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Abstract

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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Luis Alvarez-Consul, Mario Garcia-Fernandez, Oscar Garcia-Prada. 2013-09-13. Coupled equations for Kähler metrics and Yang-Mills connections. https://doi.org/10.2140/gt.2013.17.2731

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