Lagrangian submanifolds in hyperkahler manifolds, Legendre transformation

Conan Leung Chinese Univ of HK

Differential Geometry mathscidoc:1608.10095

JDG, 61, 107-145, 2002
We develop the foundation of the complex symplectic geometry of Lagrangian subvarieties in a hyperk¨ahler 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 hyperk¨ahler manifolds. We give a Pl¨ucker type formula for Lagrangian intersections under this transformation.
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  title={Lagrangian submanifolds in hyperkahler manifolds, Legendre transformation},
  author={Conan Leung},
Conan Leung. Lagrangian submanifolds in hyperkahler manifolds, Legendre transformation. 2002. Vol. 61. In JDG. pp.107-145.
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