Hamiltonian stationary tori in the complex projective plane

Abstract

We analyze here Hamiltonian stationary surfaces in the complex projective plane as (local) solutions to an integrable system, formulated as a zero curvature on a loop group. As an application, we show in details why such tori are finite type solutions, and eventually describe the simplest of them: the homogeneous ones.

Published version. Infinitesimal changes from preprint version

References in corpus (2)

• Totally Real Minimal Tori in $C{P}^2$
• Minimal tori in five-dimensional sphere in $C^3$

Cited by in corpus (11)

• Contact stationary Legendrian surfaces in $S^5$
• Twistors, 4-symmetric spaces and integrable systems
• Submanifolds and differential forms on Carnot manifolds, after M. Gromov and M. Rumin
• Rigidity of closed CSL submanifolds in the unit sphere
• Complex and Lagrangian surfaces of the complex projective plane via Kählerian Killing Spin${}^c$ spinors
• Hamiltonian-minimal submanifolds in Kaehler manifolds with symmetries
• Minimal Lagrangian surfaces in the two dimensional complex quadric via the loop group method
• The existence of Hamiltonian stationary Lagrangian tori in Kahler manifolds of any dimension
• Construction of Hamiltonian-stationary Lagrangian submanifolds of constant curvature $\epsilon$ in complex space forms $\tilde M^n(4\varepsilon)
• Spectral data for Hamiltonian-minimal Lagrangian tori in $C{P}^2$
• Construction of Hamiltonian-minimal Lagrangian submanifolds in complex Euclidean space