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An R-space is a compact homogeneous space obtained as an orbit of the isotropy representation of a Riemannian symmetric space. It is known that each R-space has the canonical embedding into a Kähler C-space as a real form, and thus a compact embedded totally geodesic Lagrangian submanifold. The minimal Maslov number of Lagrangian submanifolds in symplectic manifolds is one of invariants under Hamiltonian isotopies and very fundamental to study the Floer homology for intersections of Lagrangian submanifolds. In this paper we show a Lie theoretic formula for the minimal Maslov number of R-spaces canonically embedded in Einstein-Kähler C-spaces, and provide some examples of the calculation by the formula.

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.

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. [ABSTRACT FROM AUTHOR]