Hamiltonian stationary Lagrangian surfaces in \(\mathbb{C}^2\)

DOI10.4310/CAG.2002.v10.n1.a5zbMath1007.53060arXivmath/0009202OpenAlexW2676311778MaRDI QIDQ1607499

Pascal Romon, Frédéric Hélein

Publication date: 16 March 2003

Published in: Communications in Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0009202

zbMATH Keywords

loop groupsymmetry groupWeierstrass representationLagrangian surfacetwisted loop groupconformal Lagrangian immersionfinite type solutionHamiltonian stationary (\(H\)-minimal)Hamiltonian stationary Lagrangian torusholomorphic potentialpolynomial loopsymplectic Euclidean affine \(4\)-space

Mathematics Subject Classification ID

Loop groups and related constructions, group-theoretic treatment (22E67) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Lagrangian submanifolds; Maslov index (53D12)

Related Items (39)

On the compactness of Hamiltonian stationary Lagrangian surfaces in Kähler surfaces ⋮ Supersymmetric harmonic maps into symmetric spaces ⋮ Simple factor dressing and the López-Ros deformation of minimal surfaces in Euclidean 3-space ⋮ Geometric interpretation of second elliptic integrable systems ⋮ Hamiltonian stationary Lagrangian surfaces in \(\mathbb C \mathbb{P}^{2}\) ⋮ Some explicit examples of Hamiltonian minimal Lagrangian submanifolds in complex space forms ⋮ Dirac tori ⋮ Intersections of quadrics, moment-angle manifolds, and Hamiltonian-minimal Lagrangian embeddings ⋮ Remarks on the Gauss images of complete minimal surfaces in Euclidean four-space ⋮ Hamiltonian-minimal Lagrangian submanifolds in Kähler manifolds with symmetries ⋮ Construction of Lagrangian submanifolds in complex hyperquadric ⋮ A new construction of Lagrangians in the complex Euclidean plane in terms of planar curves ⋮ On Hamiltonian stationary Lagrangian spheres in non-Einstein Kähler surfaces ⋮ On the regularity of Hamiltonian stationary Lagrangian submanifolds ⋮ Hamiltonian stationary tori in Kähler manifolds ⋮ The existence of Hamiltonian stationary Lagrangian tori in Kähler manifolds of any dimension ⋮ On Hamiltonian minimality of isotropic non-homogeneous tori in $\mathbb{H}^n$ and $\mathbb{C} \mathrm{P}^{2n+1}$ ⋮ Hamiltonian-stationary Lagrangian surfaces of constant curvature \(\varepsilon \) in complex space form \(\tilde M ^2(4\varepsilon )\) ⋮ Classification of a family of Hamiltonian-stationary Lagrangian submanifolds in \(\mathbb C^{n}\) ⋮ On Hamiltonian-minimal isotropic homogeneous tori in \(\mathbb{C}^n\) and \(\mathbb{C}P^n\) ⋮ Classification of Hamiltonian-stationary Lagrangian submanifolds of constant curvature in \(\mathbb CP^3\) with positive relative nullity ⋮ Lagrangian surfaces in the complex hyperquadric \(Q_2\) ⋮ TRANSLATING SOLITONS FOR LAGRANGIAN MEAN CURVATURE FLOW IN COMPLEX EUCLIDEAN PLANE ⋮ Hamiltonian stationary self-similar solutions for Lagrangian mean curvature flow in the complex Euclidean plane ⋮ Elliptic Integrable Systems: a Comprehensive Geometric Interpretation ⋮ Warped product decompositions of real space forms and Hamiltonian-stationary Lagrangian submanifolds ⋮ The spectral data for Hamiltonian stationary Lagrangian tori in \(\mathbb R^4\) ⋮ Hamiltonian minimal submanifolds in complex hyperbolic space with \(SO(n)\)-symmetry ⋮ Lagrangian surfaces with circle symmetry in the complex two-space ⋮ Darboux transforms and spectral curves of Hamiltonian stationary Lagrangian tori ⋮ Examples of Hamiltonian stationary Lagrangian tori in \(\mathbb CP^2\) ⋮ Cyclic and ruled Lagrangian surfaces in Euclidean four space ⋮ Spectral data for Hamiltonian-minimal Lagrangian tori in \(\mathbb CP^{2}\) ⋮ Twistors, 4-symmetric spaces and integrable systems ⋮ Generalized DPW method and an application to isometric immersions of space forms ⋮ Equivariant gluing constructions of contact stationary Legendrian submanifolds in \({\mathbb {S}^{2n+1}}\) ⋮ Minimal Legendrian Surfaces in the Five-Dimensional Heisenberg Group ⋮ On indefinite special Lagrangian submanifolds in indefinite complex Euclidean spaces ⋮ Geometric structures on moment-angle manifolds

This page was built for publication: Hamiltonian stationary Lagrangian surfaces in \(\mathbb{C}^2\)