A new construction of Lagrangians in the complex Euclidean plane in terms of planar curves

DOI10.1016/J.GEOMPHYS.2013.10.002zbMath1301.53082arXiv1307.2152OpenAlexW2004576962MaRDI QIDQ391165

Ildefonso Castro, Ana M. Lerma

Publication date: 10 January 2014

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.2152

zbMATH Keywords

minimal surfacesolitonLagrangian submanifoldWillmore surfacecomplex planeCMC surface

Mathematics Subject Classification ID

Lagrangian submanifolds; Maslov index (53D12) Local submanifolds (53B25)

Cites Work

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• The total squared curvature of closed curves
• Calibrated geometries
• Lagrangian submanifolds of \(C^n\) with conformal Maslov form and the Whitney sphere
• Volume minimization of Lagrangian submanifolds under Hamiltonian deformations
• Construction of many Hamiltonian stationary Lagrangian surfaces in Euclidean four-space
• Hamiltonian stationary Lagrangian surfaces in \(\mathbb{C}^2\)
• Minimizing area among Lagrangian surfaces: the mapping problem.
• Construction of Hamiltonian-minimal Lagrangian submanifolds in complex Euclidean space
• Mirror symmetry is \(T\)-duality
• Lagrangian surfaces in complex Euclidean plane via spherical and hyperbolic curves
• Hamiltonian stationary self-similar solutions for Lagrangian mean curvature flow in the complex Euclidean plane
• The geometry of the generalized Gauss map
• A characterization of the Lagrangian pseudosphere
• TRANSLATING SOLITONS FOR LAGRANGIAN MEAN CURVATURE FLOW IN COMPLEX EUCLIDEAN PLANE
• Willmore surfaces on \(\mathbb{R}^4\) and the Whitney sphere

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