  In this paper we describe the cohomogeneity one special Lagrangian 3-folds in
the cotangent bundle of the 3-sphere, also known in the physics literature as a
deformed conifold. Our main result gives a global foliation of the deformed
conifold by T^2-invariant special Lagrangian 3-folds, where the generic leaf is
topologically T^2 X R. In the limit, these special Lagrangians asymptotically
approach a special Lagrangian cone on a torus in the conifold. Using moment map
techniques we also recover the family of SO(n)-invariant special Lagrangian
n-folds in the cotangent bundle of the n-sphere obtained by H. Anciaux.

Differential Geometry