非紧Gauduchon流形上的twisted Higgs丛

Q3 Mathematics 中国科学:数学 Pub Date : 2023-07-01 DOI:10.1360/ssm-2023-0114

Zhangpeng Pan, Xi Zhang

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引用次数: 0

摘要

本文研究了一类非紧化高杜川流形上扭曲希格斯束上正则度量的存在性。当扭曲的希格斯束是稳定的，我们证明在它上面一定存在厄米-爱因斯坦度规。当扭曲的希格斯束是半稳定的，我们证明了在它上面有一个近似的厄米-爱因斯坦结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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非紧Gauduchon流形上的twisted Higgs丛

In this paper, we study the existence of canonical metrics on twisted Higgs bundles over a class of noncompact Gauduchon manifolds. When the twisted Higgs bundle is stable, we prove that there must exists a Hermitian{Einstein metric on it. When the twisted Higgs bundle is semi-stable, we prove that there is an approximate Hermitian{Einstein structure on it.

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