Abstract
AbstractThe 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.
Highlights
This is a survey article based on our joint work [17]
The Gauss images of isoparametric hypersufaces of the standard sphere Sn+ provide a rich class of compact minimal Lagrangian submanifolds embedded in the complex hyperquadric Qn(C)
The isoparametric hypersurface has been well-investigated in submanifold theory and it has several nice structures and properties in di erential geometry and from the viewpoint of di erential topology, Lie theory, partial di erential equations, integrable systems and mathematical physics
Summary
This is a survey article based on our joint work [17]. The aim of our work is to build a bridge between the symplectic geometry and the submanifold theory. We mean the Floer theory for Lagrangian intersections, and by submanifold theory, isoparametric hypersurface theory. For a Lagrangian submanifold L of a symplectic manifold (M, ω), consider a Hamiltonian di eomorphism φ of M with transverse intersection L ∩ φ(L).
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