Construction of Hamiltonian-minimal Lagrangian submanifolds in complex Euclidean space

preprint2010arXivOpen access

Abstract

We describe several families of Lagrangian submanifolds in the complex Euclidean space which are H-minimal, i.e. critical points of the volume functional restricted to Hamiltonian variations. We make use of various constructions involving planar, spherical and hyperbolic curves, as well as Legendrian submanifolds of the odd-dimensional unit sphere.

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