Coupled equations for Kähler metrics and Yang-Mills connections

Details Coupled equations for Kähler metrics and Yang-Mills connections Coupled equations for Kähler metrics and Yang-Mills connections

2011-02-04

arxiv.org/abs/1102.0991v2

Mathematics

Differential Geometry

60 pages; v2: introduction partially rewritten; minor corrections and improvements in presentation, especially in Section 4; a

Scientific paper

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