  We generalize the notion of calibrated submanifolds to smooth maps and show
that the several examples of smooth maps appearing in the differential geometry
become the examples of our situation. Moreover, we apply these notion to give
the lower bound to the energy of smooth maps in the given homotopy class
between Riemannian manifolds, and consider the energy functional which is
minimized by the identity maps on the Riemannian manifolds with special
holonomy groups.
