Premium
Hamiltonian Stationary Tori in the Complex Projective Plane
Author(s) -
Hélein Frédéric,
Romon Pascal
Publication year - 2005
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s002461150401500x
Subject(s) - mathematics , integrable system , hamiltonian system , torus , projective plane , hamiltonian (control theory) , curvature , homogeneous , pure mathematics , projective test , mathematical analysis , plane curve , geometry , combinatorics , mathematical optimization , correlation
Hamiltonian stationary Lagrangian surfaces are Lagrangian surfaces in a four‐dimensional Kähler manifold which are critical points of the area functional for Hamiltonian infinitesimal deformations. In this paper we analyze these surfaces in the complex projective plane: in a previous work we showed that they correspond locally to solutions to an integrable system, formulated as a zero curvature on a (twisted) loop group. Here we give an alternative formulation, using non‐twisted loop groups and, as an application, we show in detail why Hamiltonian stationary Lagrangian tori are finite type solutions, and eventually describe the simplest of them: the homogeneous ones. 2000 Mathematics Subject Classification 53C55 (primary), 53C42, 53C25, 58E12 (secondary).