Hermitian-einstein connections on principal bundles over flat affine manifolds

Indranil Biswas, John Loftin

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Let M be a compact connected special flat affine manifold without boundary equipped with a Gauduchon metric g and a covariant constant volume form. Let G be either a connected reductive complex linear algebraic group or the real locus of a split real form of a complex reductive group. We prove that a flat principal G-bundle E G over M admits a HermitianEinstein structure if and only if E G is polystable. A polystable flat principal G-bundle over M admits a unique HermitianEinstein connection. We also prove the existence and uniqueness of a HarderNarasimhan filtration for flat vector bundles over M. We prove a Bogomolov type inequality for semistable vector bundles under the assumption that the Gauduchon metric g is astheno-Kähler.

Original languageEnglish (US)
Article number12500395
JournalInternational Journal of Mathematics
Issue number4
StatePublished - Apr 2012

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


  • Flat affine manifold
  • HarderNarasimhan filtration
  • HermitianEinstein connection
  • principal bundle


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