A Brief Note on Special Lagrangian Submanifolds in ℝ²ⁿ

Graham Smith

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Submission date: 03. Sep. 2007
Pages: 14
Bibtex
MSC-Numbers: 53C38, 35J60, 53C43, 53D12, 14M15
Keywords and phrases: special Lagrangian, Grassmannian, harmonic maps
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Abstract:
We study the differential geometry of the Grassmannian of Lagrangian subspaces in , exhibiting in particular a convex funcion whose sublevel set is the space of positive (i.e. spacelike or null) Lagrangian subspaces. We then show how a special Lagrangian immersion in induces a harmonic immersion in this Grassmannian which allowing us to obtain a rigidity result for positive special Lagrangian submanifolds which are null on a single point.