ScalingStacks

Definition 0.1 . [02YS]

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Definition 0.1.

Let XX be an nn-dimensional Calabi-Yau manifold with ω\omega the Kähler form of a Ricci-flat metric on XX and Ω\Omega a nowhere vanishing holomorphic nn-form. Then a submanifold M⊆XM\subseteq X is special Lagrangian if it is Lagrangian, i.e., dimℝM=dimℂX\dim_{\mathbb{R}}M=\dim_{\mathbb{C}}X and ω|M=0\omega|_{M}=0, and in addition, Im⁡Ω|M=0\operatorname{Im}\Omega|_{M}=0.

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