Hamiltonian stationary tori in the complex projective plane

• Autores: Frédéric Hélein, Pascal Romon
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 90, Nº 2, 2005, págs. 472-496
• Idioma: inglés
• DOI: 10.1112/s002461150401500x
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• Resumen

  • 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.