In this paper we use Lie group actions on noncompact Riemannian manifolds with calibrations to construct calibrated submanifolds. In particular, if we have an (n-1)-torus acting on a noncompact Calabi-Yau n-fold with a trivial first cohomology, then we have a special Lagrangian fibration on that n-fold. 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 construct coassociative submanifolds, and we exhibit some new examples of coassociative submanifolds via this setup. [References: 23]
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