Higgs Bundles and Flat Connections Over Compact Sasakian Manifolds
Higgs Bundles and Flat Connections Over Compact Sasakian Manifolds
复制标题
紧凑 Sasakian 流形上的希格斯束和扁平连接
DOI：
10.1007/s00220-021-04056-4
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发表时间：
2021
影响因子：
2.4
通讯作者：
Kasuya Hisashi
中科院分区：
文献类型：
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作者：
Biswas Indranil;Kasuya Hisashi
给定紧致Kähler流形dx，在完全可约平面向量束onx和多可约希格斯束onx with(Simpson，数学学报1(4):863 - 918,1988；[J]地球物理学报，2004；Uhlenbeck和Yau在common Pure applied mathematics 39:257-293, 1986；唐纳森，杜克数学，54(1):231-247,1987)。我们将范畴的等价推广到紧的Sasakian流形。证明了紧形Sasakian流形上具有平凡的一、二基本陈氏类的半简单平面向量束的范畴与具有平凡的一、二基本陈氏类的多稳定基希格斯束的范畴是等价的。我们还证明了紧化Sasakian流形上的任何稳定的基本希格斯束都存在满足Yang-Mills-Higgs方程的基本厄米度规。
Given a compact Kähler manifoldX, there is an equivalence of categories between the completely reducible flat vector bundles onXand the polystable Higgs bundlesonXwith(Simpson in J Am Math Soc 1(4):867–918, 1988; Corlette in J Differ Geom 28:361–382, 1988; Uhlenbeck and Yau in Commun Pure Appl Math 39:257–293, 1986; Donaldson in Duke Math J 54(1):231–247, 1987). We extend this equivalence of categories to the context of compact Sasakian manifolds. We prove that on a compact Sasakian manifold, there is an equivalence between the category of semi-simple flat vector bundles on it and the category of polystable basic Higgs bundles on it with trivial first and second basic Chern classes. We also prove that any stable basic Higgs bundle over a compact Sasakian manifold admits a basic Hermitian metric that satisfies the Yang–Mills–Higgs equation.