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

Henri Anciaux (1) , Ildefonso Castro (2) , Pascal Romon (3)

1 IMPA - Instituto Nacional de Matemática Pura e Aplicada
2 Departamento Matemáticas - Departamento Matemáticas
3 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Mots clés: Hamiltonian stationary.; Lagrangian submanifold; special Lagrangian; self-similar; Hamiltonian stationary

Domaines: Géométrie différentielle [math.DG]

Henri Anciaux, Ildefonso Castro, Pascal Romon. Lagrangian submanifolds foliated by (n-1)-spheres in R^2n. Acta Mathematica Sinica English Series, 2006, 22 (4), pp.1197-1214. ⟨10.1007/s10114-005-0690-6⟩. ⟨hal-00001075⟩