Lagrangian submanifolds foliated by (n-1)-spheres in R^2n
Differential Geometry
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0401372,
title = {Lagrangian submanifolds foliated by (n-1)-spheres in R^2n},
author = {Henri Anciaux and Ildefonso Castro and Pascal Romon},
journal= {arXiv preprint arXiv:math/0401372},
year = {2007}
}