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May, 2002 Lagrangian Submanifolds in Hyperkähler Manifolds, Legendre Transformation
Naichung Conan Leung
J. Differential Geom. 61(1): 107-145 (May, 2002). DOI: 10.4310/jdg/1090351322


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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Naichung Conan Leung. "Lagrangian Submanifolds in Hyperkähler Manifolds, Legendre Transformation." J. Differential Geom. 61 (1) 107 - 145, May, 2002.


Published: May, 2002
First available in Project Euclid: 20 July 2004

zbMATH: 1057.53034
MathSciNet: MR1949786
Digital Object Identifier: 10.4310/jdg/1090351322

Rights: Copyright © 2002 Lehigh University

Vol.61 • No. 1 • May, 2002
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