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Calibrated Submanifolds of R^7 and R^8 with Symmetries

Jason Lotay
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Abstract

The principal theory of this paper comprises a technique for constructing associative, coassociative and Cayley submanifolds of Euclidean space with symmetries, using first-order ordinary differential equations. Explicit examples of U(1)-invariant associative cones in R^7 and SU(2)-invariant Cayley 4-folds in R^8 are then produced using this method. Further examples of associative 3-folds are presented, which are ruled, and other systems of differential equations defining calibrated submanifolds in R^7 and R^8 are given.

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Jason Lotay. 2007-01-16. Calibrated Submanifolds of R^7 and R^8 with Symmetries. https://doi.org/10.1093/qmath/hal015

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