自偶几乎-凯勒四漫游

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2024-05-19 DOI:10.1007/s10455-024-09958-9

Inyoung Kim

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引用次数: 0

摘要

我们对正型和零型的紧凑自偶近-凯勒四流形进行了分类。特别是，利用勒布伦的结果，我们证明了任何与 \({{\mathbb {C}}}{{\mathbb {P}}}_{2}\) 差同的流形上的自偶近-凯勒度量都是\({{\mathbb {C}}}{{\mathbb {P}}}}_{2}\) 上的富比尼-斯图迪度量，直到重缩放。在负类型的情况下，我们分类了具有 J 不变里奇张量的紧凑自偶近凯勒四芒星。

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Self-dual almost-Kähler four-manifolds

We classify compact self-dual almost-Kähler four-manifolds of positive type and zero type. In particular, using LeBrun’s result, we show that any self-dual almost-Kähler metric on a manifold which is diffeomorphic to \({{\mathbb {C}}}{{\mathbb {P}}}_{2}\) is the Fubini-Study metric on \({{\mathbb {C}}}{{\mathbb {P}}}_{2}\) up to rescaling. In case of negative type, we classify compact self-dual almost-Kähler four-manifolds with J-invariant ricci tensor.

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来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.