Bundle Constructions of Calibrated Submanifolds in R^7 and R^8
arXiv:math/0408005
Abstract
We construct calibrated submanifolds of R^7 and R^8 by viewing them as total spaces of vector bundles and taking appropriate sub-bundles which are naturally defined using certain surfaces in R^4. We construct examples of associative and coassociative submanifolds of R^7 and of Cayley submanifolds of R^8. This construction is a generalization of the Harvey-Lawson bundle construction of special Lagrangian submanifolds of R^{2n}.
22 pages; for Revised Version: Minor changes, improved notation, streamlined exposition