Lagrangian geometry of the Gauss images of isoparametric hypersurfaces in spheres

Abstract

The Gauss images of isoparametric hypersufaces of the standard sphere Sn+1 provide a rich class of compact minimal Lagrangian submanifolds embedded in the complex hyperquadric Qn(ℂ). This is a survey article based on our joint work [17] to study the Hamiltonian non-displaceability and related properties of such Lagrangian submanifolds.

Keywords

• isoparametric hypersurfaces
• monotone lagrangian submanifolds
• floer homology
• primary: 53c40
• secondary: 53c42, 53d12