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

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

2006-01-31

arxiv.org/abs/math/0601764v2

Q J Math, March 2007; 58: 53 - 70.

Mathematics

Differential Geometry

21 pages, minor corrections, section added containing further systems of differential equations defining calibrated submanifol

Scientific paper

10.1093/qmath/hal015

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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