Hamiltonian-minimal Lagrangian submanifolds in Kaehler manifolds with symmetries

By making use of the symplectic reduction and the cohomogeneity method, we give a general method for constructing Hamiltonian minimal Lagrangian submanifolds in Kaehler manifolds with symmetries. As applications, we construct infinitely many nontrivial complete Hamiltonian minimal Lagrangian submanifolds in CPⁿ$C{P}^n$ and Cⁿ$C^n$.