Special Lagrangian Geometry in irreducible symplectic 4-folds
نویسنده
چکیده
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 obtained by complex submanifolds via a generalization of the so called hyperkaehler rotation trick; thus they retain part of the rigidity of the complex submanifolds: indeed all special Lagrangian submanifolds of X turn out to be real analytic. MSC (1991): Primary: 53C15, Secondary: 53A40, 51P05, 53C20
منابع مشابه
Addendum To: On fibre space structures of a projective irreducible symplectic manifold
Remark. Beauville proves that a Lagrangian fibration is a complete integrable system in [2, Proposition 1]. Thus, a general fibre of a fibre space of a projective irreducible symplectic manifold is an abelian variety. Remark. Markshevich states in [4, Remark 3.2] that there exists an irreducible symplectic manifold which has a family of non lagrangian tori. But this family does not form fibration.
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