Warped product decompositions of real space forms and Hamiltonian-stationary Lagrangian submanifolds

A Lagrangian submanifold of a Kaehler manifold is said to be Hamiltonian-stationary (or HH-stationary for short) if it is a critical point of the area functional restricted to compactly supported Hamiltonian variations. In this article, we present some simple relationship between warped product decompositions of real space forms and Hamiltonian-stationary Lagrangian submanifolds. We completely classify HH-stationary Lagrangian submanifolds in complex space forms arisen from warped product decompositions. More precisely, we prove that there exist two such families of HH-stationary Lagrangian submanifolds in Cn, two families in CPnCPn, and twenty-one families in CHnCHn. As immediate by-product we obtain many new families of Hamiltonian-stationary Lagrangian submanifolds in complex space forms.