Mathematical Research Letters

Volume 12 (2005)

Number 4

Bundle Constructions of Calibrated Submanifolds in $\mathbb R^7$ and $\mathbb R^8$

Pages: 493 – 512

DOI: http://dx.doi.org/10.4310/MRL.2005.v12.n4.a5

Authors

Marianty Ionel

Spiro Karigiannis

Maung Min-Oo

Abstract

We construct calibrated submanifolds of $\mathbb R^7$ and $\mathbb R^8$ by viewing them as total spaces of vector bundles and taking appropriate sub-bundles which are naturally defined using certain surfaces in $\mathbb R^4$. We construct examples of associative and coassociative submanifolds of $\mathbb R^7$ and of Cayley submanifolds of $\mathbb R^8$. This construction is a generalization of the Harvey-Lawson bundle construction of special Lagrangian submanifolds of $\mathbb C^{n}$.

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