Journal of Differential Geometry

Lagrangian Submanifolds in Hyperkähler Manifolds, Legendre Transformation

Naichung Conan Leung


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 normalized Legendre transformation of Lagrangian subvarieties under a birational transformation of projective hyperkähler manifolds. We give a Plücker type formula for Lagrangian intersections under this transformation.

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J. Differential Geom., Volume 61, Number 1 (2002), 107-145.

First available in Project Euclid: 20 July 2004

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Leung, Naichung Conan. Lagrangian Submanifolds in Hyperkähler Manifolds, Legendre Transformation. J. Differential Geom. 61 (2002), no. 1, 107--145. doi:10.4310/jdg/1090351322.

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