This paper is a continuation of math.DG/0408005. We first construct specialLagrangian submanifolds of the Ricci-flat Stenzel metric (of holonomy SU(n)) onthe cotangent bundle of S^n by looking at the conormal bundle of appropriatesubmanifolds of S^n. We find that the condition for the conormal bundle to bespecial Lagrangian is the same as that discovered by Harvey-Lawson forsubmanifolds in R^n in their pioneering paper. We also construct calibratedsubmanifolds in complete metrics with special holonomy G_2 and Spin(7)discovered by Bryant and Salamon on the total spaces of appropriate bundlesover self-dual Einstein four manifolds. The submanifolds are constructed ascertain subbundles over immersed surfaces. We show that this constructionrequires the surface to be minimal in the associative and Cayley cases, and tobe (properly oriented) real isotropic in the coassociative case. We also makesome remarks about using these constructions as a possible local model for theintersection of compact calibrated submanifolds in a compact manifold withspecial holonomy.
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