Darboux transforms and spectral curves of Hamiltonian stationary Lagrangian tori - Laboratoire d'Analyse et de Mathématiques Appliquées Accéder directement au contenu
Article Dans Une Revue Calculus of Variations and Partial Differential Equations Année : 2010

Darboux transforms and spectral curves of Hamiltonian stationary Lagrangian tori

Résumé

The multiplier spectral curve of a conformal torus in the 4-sphere is essentially, see arXiv:0712.2311, given by all Darboux transforms of the conformal torus. In the particular case when the conformal immersion is a Hamiltonian stationary torus in Euclidean 4-space, the left normal of the immersion is harmonic, hence we can associate a second Riemann surface: the eigenline spectral curve of the left normal, as defined by Hitchin. We show that the multiplier spectral curve of a Hamiltonian stationary torus and the eigenline spectral curve of its left normal are biholomorphic Riemann surfaces of genus zero. Moreover, we prove that all Darboux transforms, which arise from generic points on the spectral curve, are Hamiltonian stationary whereas we also provide examples of Darboux transforms which are not even Lagrangian.

Dates et versions

hal-00288862 , version 1 (18-06-2008)

Identifiants

Citer

Katrin Leschke, Pascal Romon. Darboux transforms and spectral curves of Hamiltonian stationary Lagrangian tori. Calculus of Variations and Partial Differential Equations, 2010, 38 (1-2), pp.45-74. ⟨10.1007/s00526-009-0278-6⟩. ⟨hal-00288862⟩
71 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More