Year: 2005
Type: article
Abstract: 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).
Authors: Frédéric Hélein, Pascal Romon
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2139224855