Construction of Hamiltonian-minimal Lagrangian submanifolds in complex Euclidean space

TL;DR

This paper constructs various Hamiltonian-minimal Lagrangian submanifolds in complex Euclidean space using geometric methods involving curves and Legendrian submanifolds, contributing new explicit examples to symplectic geometry.

Contribution

It introduces new families of H-minimal Lagrangian submanifolds constructed via planar, spherical, hyperbolic curves, and Legendrian submanifolds, expanding known examples in symplectic geometry.

Findings

Explicit constructions of H-minimal Lagrangian submanifolds

Use of curves and Legendrian submanifolds in constructions

New examples enriching the theory of Hamiltonian-minimal submanifolds

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.