non abelian hodge correspondance I Harmonic bundle let F le a vector space Met F positive definite quadratic forms on f is aRiemannian manifold Tg Mett F A CEnd E symmetric W r log A 137g AB A harmonic metric on a flat bundle Fis a harmonic section of Met F M A harmonic bundle ED g is a flat bundle CE D together with a harmonic metric g II harmonic bundles andrepresentations Harmonic bundles Repli s Ghm R Theorem Colette Donaldson Let Mbe a complete Riemannian let p tu Glen R assume is reductive then there exists an Essentially unique harmonic metric on Ep essentially unique g g CA A J with D'A 0 Next goal relate harmonic bundle to Higgs bundles and extend the theory to other semi simple G crash case on symmetric spaces
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non abelian hodge correspondance
I Harmonicbundle
let F le avectorspace Met F positivedefinitequadratic formson fis aRiemannianmanifold Tg MettF ACEndE symmetric W r log
A 137g ABAharmonicmetricon a flatbundle Fis a harmonicsectionof
Met F M
A harmonic bundle E Dg is a flatbundleCED togetherwith