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2004•arXiv (Cornell University)Open access

Lagrangian submanifolds foliated by (n-1)-spheres in R^2n

Henri Anciaux, Ildefonso Castro, Pascal Romon

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Abstract

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.

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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.

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Available abstract

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.

Key concepts: Submanifold, Lagrangian, SPHERES, Parametrization (atmospheric modeling), Ode, Hamiltonian (control theory), Mathematics, Invariant (physics)

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