Abstract
In this article we shall provide a survey of our recent works and their environs on differential geometry of Lagrangian submanifolds in specific Kahler manifolds such as complex projective spaces, complex space forms, Hermitian symmetric spaces and so on. We shall emphasis on the relationship between certain minimal Lagrangian submanifold in complex hyperquadrics and isoparametric hypersurfaces in spheres. We shall discuss their properties and related problems of the Gauss images of isoparametric hypersurfaces. This article is mainly based on my joint work with Hui Ma (Tsinghua University, Beijing).
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