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Hamiltonian Stationary Tori in the Complex Projective Plane 总被引:3,自引:0,他引:3
Hamiltonian stationary Lagrangian surfaces are Lagrangian surfacesin a four-dimensional Kähler manifold which are criticalpoints of the area functional for Hamiltonian infinitesimaldeformations. In this paper we analyze these surfaces in thecomplex projective plane: in a previous work we showed thatthey correspond locally to solutions to an integrable system,formulated as a zero curvature on a (twisted) loop group. Herewe give an alternative formulation, using non-twisted loop groupsand, as an application, we show in detail why Hamiltonian stationaryLagrangian tori are finite type solutions, and eventually describethe simplest of them: the homogeneous ones. 2000 MathematicsSubject Classification 53C55 (primary), 53C42, 53C25, 58E12(secondary). 相似文献
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