Torus invariant special Lagrangian submanifolds in the canonical bundle of toric positive Kähler Einstein manifolds

Abstract

In this paper we construct torus invariant special Lagrangian submanifolds in the canonical bundle K_M of the toric positive Kähler Einstein manifold M. We construct a Ricci-flat metric on K_M using the Calabi ansatz to show that K_M is a Calabi-Yau manifold. Then, using moment map techniques developed in [6], we construct special Lagrangian submanifolds in K_M.