Coupled equations for Kähler metrics and Yang-Mills connections. (English) Zbl 1275.32019
Summary: We study equations on a principal bundle over a compact complex manifold coupling a connection on the bundle with a Kähler structure on the base. These equations generalize the conditions of constant scalar curvature for a Kähler 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.
MSC:
| 32Q15 | Kähler manifolds |
| 53C07 | Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) |
Keywords:
coupled Kähler-Yang-Mills equation; Hermitian-Yang-Mills connection; generalized Futaki invariant; generalized Mabuchi energyReferences:
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