Special Lagrangian submanifolds invariant under the isotropy action of symmetric spaces of rank two

Abstract

We study special Lagrangian submanifolds of the cotangent bundle $T^*S^n$ of the sphere in the tangent space of Riemannian symmetric space of rank two. We show that the special Lagrangian submanifolds correspond to the solution of a differential equation on $\mathbb{R}^2$ under the assumption that the submanifold is of cohomogeneity one. Our result is the generalization of the former work of Sakai and the first author [5]. We study the qualitative properties of the solution for the special Lagrangian submanifolds and give some examples.