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Coupled equations for Kähler metrics and Yang-Mills connections

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  • Mario Garcia Fernandez, Denmark
  • Luis Alvarez-Consul, ICMAT, CSIC (MADRID), Spain
  • Oscar Garcia-Prada, ICMAT, CSIC (MADRID), Spain
We study equations on a principal bundle over a compact complex manifold
coupling connections on the bundle with K¨ahler structures in 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,
Mabuchi functional and geodesic stability. We finish by giving some examples of solutions.
Original languageEnglish
Number of pages58
Publication statusPublished - 2012

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