Higgs bundles over foliation manifolds

Science China Mathematics volume 64, pages399–420(2021)Cite this article

Abstract

In this paper, we consider the stability, semi-stability and canonical metric structures on transverse Higgs bundles over a class of foliation manifolds, also a transversal Bogomolov inequality is obtained.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11625106, 11571332 and 11721101).

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Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China

    Di Wu & Xi Zhang

Authors
  1. Di Wu
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  2. Xi Zhang
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Correspondence to Xi Zhang.

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Wu, D., Zhang, X. Higgs bundles over foliation manifolds. Sci. China Math. 64, 399–420 (2021). https://doi.org/10.1007/s11425-019-1736-4

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Keywords

  • foliation manifold
  • Higgs bundle
  • (approximate) transverse Hermitian-Einstein
  • transversal Bogomolov inequality

MSC(2010)

  • 53C07
  • 53C12
  • 53C25
  • 58E15