13 research outputs found
Cohomogeneity One Special Lagrangian Submanifolds in the Deformed Conifold
In this paper we describe the cohomogeneity one special Lagrangian 3-folds in
the cotangent bundle of the 3-sphere, also known in the physics literature as a
deformed conifold. Our main result gives a global foliation of the deformed
conifold by T^2-invariant special Lagrangian 3-folds, where the generic leaf is
topologically T^2 X R. In the limit, these special Lagrangians asymptotically
approach a special Lagrangian cone on a torus in the conifold. Using moment map
techniques we also recover the family of SO(n)-invariant special Lagrangian
n-folds in the cotangent bundle of the n-sphere obtained by H. Anciaux.Comment: 22 pages, 2 figure
Bundle Constructions of Calibrated Submanifolds in R^7 and R^8
We construct calibrated submanifolds of R^7 and R^8 by viewing them as total
spaces of vector bundles and taking appropriate sub-bundles which are naturally
defined using certain surfaces in R^4. We construct examples of associative and
coassociative submanifolds of R^7 and of Cayley submanifolds of R^8. This
construction is a generalization of the Harvey-Lawson bundle construction of
special Lagrangian submanifolds of R^{2n}.Comment: 22 pages; for Revised Version: Minor changes, improved notation,
streamlined expositio