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Annals of Global Analysis and Geometry

, Volume 47, Issue 1, pp 1–11 | Cite as

Approximate Hermitian–Yang–Mills structures on semistable principal Higgs bundles

  • Ugo BruzzoEmail author
  • Beatriz Graña OteroEmail author
Article

Abstract

We generalize the Hitchin–Kobayashi correspondence between semistability and the existence of approximate Hermitian–Yang–Mills structures to the case of principal Higgs bundles. We prove that a principal Higgs bundle \({\mathfrak {E}}\) on a compact Kähler manifold, with structure group a connected linear algebraic reductive group \(G\), is semistable if and only if it admits an approximate Hermitian–Yang–Mills structure.

Keywords

Principal (Higgs) bundles Semistability Approximate Hermitian–Yang–Mills structures Hermitian–Yang–Mills metrics 

Mathematics Subject Classification

53C07 32L05 14F05 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Scuola Internazionale Superiore di Studi AvanzatiTriesteItaly
  2. 2.Sezione di TriesteIstituto Nazionale di Fisica NucleareTriesteItaly
  3. 3.Departamento de MatemáticasPontificia Universidad JaverianaBogotáColombia

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