Calibrated Submanifolds of R^7 and R^8 with Symmetries
Abstract
Description
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.
21 pages, minor corrections, section added containing further systems of differential equations defining calibrated submanifolds
21 pages, minor corrections, section added containing further systems of differential equations defining calibrated submanifolds