Annals of Global Analysis and Geometry

, Volume 48, Issue 4, pp 345–355 | Cite as

A note on semistable Higgs bundles over compact Kähler manifolds

  • Yanci Nie
  • Xi ZhangEmail author


In this note, by using the Yang–Mills–Higgs flow, we show that semistable Higgs bundles with vanishing first and second Chern numbers over compact Käher manifolds must admit a filtration whose quotients are Hermitian flat Higgs bundles. This generalizes a result of Simpson for compact projective manifolds to the compact Kähler case.


Higgs bundle Filtration Yang–Mills–Higgs flow 

Mathematics Subject Classification

53C07 58E15 


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of Science and Technology of ChinaHefeiPeople’s Republic of China
  2. 2.Key Laboratory of Wu Wen-Tsun Mathematics, Chinese Academy of Sciences, School of Mathematical SciencesUniversity of Science and Technology of ChinaHefeiPeople’s Republic of China

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