| Some Remarks on Higgs Bundles over Compact Generalized K\"{a}hler Manifolds |
| Received:April 28, 2020 Revised:June 26, 2021 |
| Key Words:
$I_{\pm}$-Higgs bundle generalized K\"{a}hler manifold Gauduchon metric $\alpha$-Hermite-Yang-Mills-Higgs metric approximate $\alpha$-Hermite-Yang-Mills-Higgs structure
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| Fund Project: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). |
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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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