  We study Lagrangian submanifolds foliated by (n-1)-spheres in R^2n for n>2.
We give a parametrization valid for such submanifolds, and refine that
description when the submanifold is special Lagrangian, self-similar or
Hamiltonian stationary. In all these cases, the submanifold is centered, i.e.
invariant under the action of SO(n). It suffices then to solve a simple ODE in
two variables to describe the geometry of the solutions.
