Cohomogeneity One Special Lagrangian Submanifolds in the Deformed Conifold

Details Cohomogeneity One Special Lagrangian Submanifolds in the Deformed Conifold Cohomogeneity One Special Lagrangian Submanifolds in the Deformed Conifold

2005-04-27

arxiv.org/abs/math/0504557v1

Mathematics

Differential Geometry

22 pages, 2 figures

Scientific paper

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.

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