We study Lagrangian submanifolds foliated by （n - 1）-spheres in R^2n for n ≥ 3. We give a general parametrization for such submanifolds, and refine that description when the submanifold is special Lagrangian, self-...We study Lagrangian submanifolds foliated by （n - 1）-spheres in R^2n for n ≥ 3. We give a general parametrization for such submanifolds, and refine that description when the submanifold is special Lagrangian, self-similar, Hamiltonian stationary or has mean curvature vector of constant length. 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.展开更多
文摘We study Lagrangian submanifolds foliated by （n - 1）-spheres in R^2n for n ≥ 3. We give a general parametrization for such submanifolds, and refine that description when the submanifold is special Lagrangian, self-similar, Hamiltonian stationary or has mean curvature vector of constant length. 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.
