The branched deformations of the special Lagrangian submanifolds
Abstract
The branched deformations of immersed compact special Lagrangian submanifolds are studied in this paper. If there exists a nondegenerate Z2 harmonic 1-form over a special Lagrangian submanifold L, we construct a family of immersed special Lagrangian submanifolds Lt, that are diffeomorphic to a branched covering of L and Lt convergence to 2L as current. This answers a question suggested by Donaldson. Combining with the work of Abouzaid and Imagi, we obtain constraints for the existence of nondegenerate Z2 harmonic 1-forms.
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