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：

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$$ {\ mathbf {C}} ^ {{n}} $$ 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 \）在\（（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。