Lagrangian submanifolds foliated by \((n-1)\)-spheres in \(\mathbb R^{2n}\)

DOI10.1007/s10114-005-0690-6zbMath1105.53060arXivmath/0401372OpenAlexW1981322141MaRDI QIDQ2508644

Henri Anciaux, Pascal Romon, Ildefonso Castro

Publication date: 13 October 2006

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0401372

zbMATH Keywords

Lagrangian submanifoldself-similarHamiltonian stationary

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Lagrangian submanifolds; Maslov index (53D12)

Related Items (7)

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 \(\mathbb C^{n}\) ⋮ Classification of Hamiltonian-stationary Lagrangian submanifolds of constant curvature in \(\mathbb CP^3\) with positive relative nullity ⋮ Construction of Hamiltonian-minimal Lagrangian submanifolds in complex Euclidean space ⋮ Construction of Lagrangian self-similar solutions to the mean curvature flow in \(\mathbb C^n\) ⋮ Two non existence results for the self-similar equation in Euclidean 3-space ⋮ Cyclic and ruled Lagrangian surfaces in Euclidean four space

Cites Work

• Calibrated geometries
• Volume minimization of Lagrangian submanifolds under Hamiltonian deformations
• Minimal Lagrangian diffeomorphisms and the Monge-Ampère equation
• Lagrangian helicoids
• Construction of many Hamiltonian stationary Lagrangian surfaces in Euclidean four-space
• On a minimal Lagrangian submanifold of \(\mathbf C^n\) foliated by spheres
• Weierstrass representation of Lagrangian surfaces in four-dimensional space using spinors and quaternions
• Riemannian geometry of Lagrangian submanifolds
• Special Lagrangian \(m\)-folds in \(\mathbb{C}^m\) with symmetries
• Construction of Lagrangian self-similar solutions to the mean curvature flow in \(\mathbb C^n\)
• A characterization of the Lagrangian pseudosphere
• On a new construction of special Lagrangian immersions in complex Euclidean space

This page was built for publication: Lagrangian submanifolds foliated by \((n-1)\)-spheres in \(\mathbb R^{2n}\)