Deformations of Special Lagrangian Submanifolds; An Approach via Fredholm Alternative

Details Deformations of Special Lagrangian Submanifolds; An Approach via Fredholm Alternative Deformations of Special Lagrangian Submanifolds; An Approach via Fredholm Alternative

2006-01-05

arxiv.org/abs/math/0601106v2

Gokova Geom-Top. (2006), No. 1,154-161, Int. Press.

Mathematics

Differential Geometry

To appear in Gokova Geometry-Topology

Scientific paper

In an earlier paper, we showed that the moduli space of deformations of a smooth, compact, orientable special Lagrangian submanifold L in a symplectic manifold X with a non-integrable almost complex structure is a smooth manifold of dimension H^1(L), the space of harmonic 1-forms on L. We proved this first by showing that the linearized operator for the deformation map is surjective and then applying the Banach space implicit function theorem. In this paper, we obtain the same surjectivity result by using a different method, the Fredholm Alternative, which is a powerful tool for compact operators in linear functional analysis.

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