Construction of Hamiltonian-minimal Lagrangian submanifolds in complex Euclidean space

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.

23 pages, 5 figures, Second version. Changes in statement and proof of Corollary 4

References in corpus (4)

• The geometric complexity of special Lagrangian $T^2$-cones
• Hamiltonian stationary tori in the complex projective plane
• Cyclic and ruled Lagrangian surfaces in complex Euclidean space
• Hamiltonian stationary self-similar solutions for Lagrangian mean curvature flow in complex Euclidean plane