Lagrangian Submanifolds in Hyperkähler manifolds, Legendre transformation
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Lagrangian Submanifolds in Hyperkähler Manifolds, Legendre Transformation
We develop the foundation of the complex symplectic geometry of Lagrangian subvarieties in a hyperkähler manifold. We establish a characterization, a Chern number inequality, topological and geometrical properties of Lagrangian submanifolds. We discuss a category of Lagrangian subvarieties and its relationship with the theory of Lagrangian intersection. We also introduce and study extensively a...
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