New examples of minimal Lagrangian tori in the complex projective plane

DOI10.1007/BF02568198zbMath0824.53059OpenAlexW1980304267MaRDI QIDQ1344912

Ildefonso Castro, Francisco Urbano

Publication date: 30 March 1995

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/156022

zbMATH Keywords

Lagrangian toricomplex projective planeholomorphic isometriescompact Lagrangian minimal surfaces

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (17)

Constructions of almost complex 2-tori of type (III) in the nearly Kähler 6-sphere ⋮ The geometric complexity of special Lagrangian \(T^2\)-cones ⋮ Minimal Legendrian submanifolds of \(S^{2n+1}\) and absolutely area-minimizing cones ⋮ On the rotation class of knotted Legendrian tori in \(\mathbb{R}^5\) ⋮ An energy functional for Lagrangian tori in \(\mathbb {C}P^2\) ⋮ On minimal isotropic tori in \(\mathbb{C}P^3\) ⋮ Minimal surfaces in spheres and a Ricci-like condition ⋮ Construction of Lagrangian submanifolds in complex hyperquadric ⋮ Ruh-Vilms theorems for minimal surfaces without complex points and minimal Lagrangian surfaces in \(\mathbb{C}P^2\) ⋮ Minimal Lagrangian surfaces in \(\mathbb{C}P^2\) via the loop group method. I: The contractible case ⋮ Lagrangian surfaces in the complex hyperquadric \(Q_2\) ⋮ On a family of conformally flat minimal Lagrangian tori in \(\mathbb CP^{3}\) ⋮ Minimal Lagrangian submanifolds in \(\mathbb{CP}^n\) with diagonal metric ⋮ Totally real minimal tori in \(\mathbb CP^2\) ⋮ Examples of Hamiltonian stationary Lagrangian tori in \(\mathbb CP^2\) ⋮ Minimal Lagrangian submanifolds in \(\mathbb{C}\mathbb{P}^3\) and the sinh-Gordon equation ⋮ Special Lagrangian \(m\)-folds in \(\mathbb{C}^m\) with symmetries

Cites Work

• The total squared curvature of closed curves
• The fundamental equations of minimal surfaces in \({\mathbb{C}}P^ 2\)
• Totally real submanifolds and symmetric bounded domains
• All constant mean curvature tori in \(R^ 3\), \(S^ 3\), \(H^ 3\) in terms of theta-functions
• On the classification of constant mean curvature tori
• Minimal Surfaces by Moving Frames
• Submanifolds with Constant Mean Curvature
• A Totally Real Surface in CP 2 that is not Totally Geodesic
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