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Uniqueness of some Calabi–Yau metrics on $${\mathbf {C}}^{{n}}$$ C n
Geometric and Functional Analysis ( IF 2.4 ) Pub Date : 2020-09-07 , DOI: 10.1007/s00039-020-00543-3
Gábor Székelyhidi

We consider the Calabi–Yau metrics on \(\mathbf {C}^n\) constructed recently by Yang Li, Conlon–Rochon, and the author, that have tangent cone \(\mathbf {C}\times A_1\) at infinity for the \((n-1)\)-dimensional Stenzel cone \(A_1\). We show that up to scaling and isometry this Calabi–Yau metric on \(\mathbf {C}^n\) is unique. We also discuss possible generalizations to other manifolds and tangent cones.



中文翻译:

$$ {\ mathbf {C}} ^ {{n}} $$ C n上某些Calabi–Yau指标的唯一性

我们认为,卡拉比-丘度量的\(\ mathbf {C} ^ N \)最近由杨力,康伦,罗雄,笔者构建的,具有切锥\(\ mathbf {C} \次A_1 \)\((n-1)\)维Stenzel锥\(A_1 \)的无穷大。我们显示,直到缩放和等轴测图,\(\ mathbf {C} ^ n \)上的Calabi–Yau度量标准都是唯一的。我们还将讨论对其他流形和切锥的可能概括。

更新日期:2020-09-08
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