Minimal Lagrangian tori in Kahler-Einstein manifolds

In this paper we use structure preserving torus actions on KahlerEinstein manifolds to construct minimal Lagrangian submanifolds. Our main result is: Let N be a Kahler-Einstein manifold with positive scalar curvature with an effective T -action. Then precisely one regular orbit L of the T -action is a minimal Lagrangian submanifold of N . Moreover there is an (n− 1)-torus T n−1 ⊂ T n and a sequence of non-flat immersed minimal Lagrangian tori Lk, invariant under T n−1 s.t. Lk locally converge to L (in particular the supremum of the sectional curvatures of Lk and the distance between L and Lk go to 0 as k 7→ ∞).