MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint

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

Graham Smith


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.

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

Related publications

2007 Repository Open Access
Graham Smith

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