Calibrated fibrations on noncompact manifolds via group actions

In this paper we use Lie group actions on noncompact Riemannian manifolds w ith calibrations to construct calibrated submanifolds. In particular, if we have an (n-1)-torus acting on a noncompact Calabi-Yau n-fold with a trivia l first cohomology, then we have a special Lagrangian fibration on that n-f old. We produce several families of examples for this construction and give some applications to special Lagrangian geometry on compact almost Calabi- Yau manifolds. We also use group actions on noncompact G(2)-manifolds to co nstruct coassociative submanifolds, and we exhibit some new examples of coa ssociative submanifolds via this setup.