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The Quarterly Journal of Mathematics Advance Access originally published online on November 9, 2006
The Quarterly Journal of Mathematics 2007 58(1):53-70; doi:10.1093/qmath/hal015
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© 2006. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

CALIBRATED SUBMANIFOLDS OF R7 AND R8 WITH SYMMETRIES

Jason Dean Lotay*

University College, Oxford OX1 4BH

* E-mail: jason.lotay{at}univ.ox.ac.uk

Received 6 February 2006;
  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 R7 and SU(2)-invariant Cayley 4-folds in R8 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 R7 and R8 are given.


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