Some Remarks on Higgs Bundles over Compact Generalized K\"{a}hler Manifolds
Received:April 28, 2020  Revised:June 26, 2021
Key Word: $I_{\pm}$-Higgs bundle   generalized K\"{a}hler manifold   Gauduchon metric   $\alpha$-Hermite-Yang-Mills-Higgs metric   approximate $\alpha$-Hermite-Yang-Mills-Higgs structure  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.11971253; 11625106; 11801535; 11721101), the Natural Science Foundation of Anhui Province (Grant No.1908085QA04) and Partially Supported by the Project ``Analysis and Geometry on Bundle" of Ministry of Science and Technology of the People's Republic of China (Grant No.SQ2020YFA070080).
Author NameAffiliation
Ruixin WANG School of Mathematical Sciences, University of Science and Technology of China, Anhui 230026, P. R. China 
Wen WANG School of Mathematics and Statistics, Hefei Normal University, Anhui 230026, P. R. China 
Songting YIN Department of Mathematics and Computer Science, Tongling University, Anhui 244000, P. R. China 
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Abstract:
      In this paper, we first solve the Dirichlet problem for $\alpha$-Hermite-Yang-Mills-Higgs equations on $I_{\pm}$-Higgs bundles over a compact generalized K\"{a}hler manifold. Then we prove that the $\alpha$-semi-stability on $I_{\pm}$-Higgs bundles over closed generalized K\"{a}hler manifolds implies the existence of approximate $\alpha$-Hermite-Yang-Mills-Higgs structure.
Citation:
DOI:10.3770/j.issn:2095-2651.2021.05.009
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