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MiS Preprint
80/2007

A Brief Note on Special Lagrangian Submanifolds in $\Bbb{R}^{2n}$

Graham Smith

Abstract

We study the differential geometry of the Grassmannian of Lagrangian subspaces in $\Bbb{R}^{2n}$, 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 $\Bbb{R}^{2n}$ 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.

Received:
Sep 3, 2007
Published:
Sep 3, 2007
MSC Codes:
53C38, 35J60, 53C43, 53D12, 14M15
Keywords:
special Lagrangian, Grassmannian, harmonic maps

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2007 Repository Open Access
Graham Smith

A brief note on special Lagrangian submanifolds in \(\mathbb{R}^{2n}\)