Calibrated subbundles in noncompact manifolds of special holonomy (Q2490346)

In the paper [Math. Res. Lett. 12, 493--512 (2005; Zbl 1089.53035)], the present authors along with \textit{M. Ionel} have generalized a bundle construction of Harvey and Lawson for special Lagrangian submanifolds in \(\mathbb C^n\) to analogous constructions of coassociative, associative, and Cayley submanifolds in \(\mathbb R^7\) and \(\mathbb R^8\). In this paper the present authors, further generalize this construction to the case of several explicit, nonflat, noncompact manifolds with complete metrics of special holonomy which are vector bundles over a compact base. The submanifolds are constructed as certain subbundles over immersed surfaces. The authors show that this construction requires the surface to be minimal in the associative and Cayley cases, and to be (properly oriented) real isotropic in the coassociative case. Finally, the authors make some remarks about how these constructions might be used as local models for the intersections of compact calibrated submanifolds of a compact manifold with special holonomy.