berglund - h bsch转置定则与sasaki几何

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2023-11-16 DOI:10.1007/s10455-023-09932-x

Ralph R. Gomez

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引用次数: 1

摘要

我们应用BHK镜像对称的berglund - h bsch转置规则，证明了在可逆多项式定义的加权投影空间中的\(n-1\)维Calabi-Yau轨道上，我们可以关联4个(可能)不同的\(2n+1\)维(\(n-1\) -连通)且允许一个正Ricci曲率度规的Sasaki流形。我们应用这个定理证明了对于给定的K3轨道，存在4个正Ricci曲率的七维sasaki流形，其中2个实际上是Sasaki-Einstein流形。

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Berglund–Hübsch transpose rule and Sasakian geometry

We apply the Berglund–Hübsch transpose rule from BHK mirror symmetry to show that to an \(n-1\)-dimensional Calabi–Yau orbifold in weighted projective space defined by an invertible polynomial, we can associate four (possibly) distinct Sasaki manifolds of dimension \(2n+1\) which are \(n-1\)-connected and admit a metric of positive Ricci curvature. We apply this theorem to show that for a given K3 orbifold, there exist four seven-dimensional Sasakian manifolds of positive Ricci curvature, two of which are actually Sasaki–Einstein.

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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.