Hamiltonian stationary Lagrangian tori in Kähler manifolds

AbstractA Hamiltonian stationary Lagrangian submanifold of a Kähler manifold is a Lagrangian submanifold whose volume is stationary under Hamiltonian variations. We find a sufficient condition on the curvature of a Kähler manifold of real dimension four to guar- antee the existence of a family of small Hamiltonian stationary Lagrangian tori.