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

摘要

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 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. We study the qualitative properties of the solution for the special Lagrangian submanifolds and give some examples.