Bundle Constructions of Calibrated Submanifolds in R7 and R8
Abstract
We construct calibrated submanifolds of R7 and R8 by viewing them as total spaces of vector bundles and taking appropriate sub-bundles which are naturally defined using certain surfaces in R4. We construct examples of associative and coassociative submanifolds of R7 and of Cayley submanifolds of R8. This construction is a generalization of the Harvey-Lawson bundle construction of special Lagrangian submanifolds of R2n.
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