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Special Lagrangian Geometry in irreducible symplectic 4-folds

Alessandro Arsie
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Abstract

Having fixed a Kaehler class and the unique corresponding hyperkaehler metric, we prove that all special Lagrangian submanifolds of an irreducible symplectic 4-fold X are bi-Lagrangian and that they are obtained by complex submanifolds via a sort of "hyperkaehler rotation trick"; thus they retain part of the rigidity of complex submanifolds: indeed all special Lagrangian submanifolds of X turn out to be real analytic.

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Alessandro Arsie. 2000-01-11. Special Lagrangian Geometry in irreducible symplectic 4-folds. https://arxiv.org/abs/math/0001060

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