Bundle Constructions of Calibrated Submanifolds in R^7 and R^8

Details Bundle Constructions of Calibrated Submanifolds in R^7 and R^8 Bundle Constructions of Calibrated Submanifolds in R^7 and R^8

2004-07-31

arxiv.org/abs/math/0408005v2

Mathematical Research Letters 12, 493-512 (2005)

Mathematics

Differential Geometry

22 pages; for Revised Version: Minor changes, improved notation, streamlined exposition

Scientific paper

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}.

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