Coupled equations for Kähler metrics and Yang-Mills connections
arXiv:1102.0991 · doi:10.2140/gt.2013.17.2731
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.
arXiv comment61 pages; v2: introduction partially rewritten; minor corrections and improvements in presentation, especially in Section 4; added references; v3: To appear in Geom. Topol. Minor corrections and improvements, following comments by referees
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