2007/05/05 by Hui Ma, Ma, Hui, Yoshihiro Ohnita +1
Mathematics · #53C40 #53C42 #53D12 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.0705.0694
openalex publication_date 2007/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The n-dimensional complex hyperquadric is a compact complex algebraic hypersurface defined by the quadratic equation in the (n+1)-dimensional complex projective space, which is isometric to the real Grassmann manifold of oriented 2- planes and is a compact Hermitian symmetric space of rank 2. In this paper we study geometry of compact Lagrangian submanifolds in complex hyperquadrics from the viewpoint of the theory of isoparametric hypersurfaces in spheres. From this viewpoint we provide a classification theorem of compact homogeneous Lagrangian submanifolds in complex hyperquadrics by using the moment map technique. Moreover we determine the Hamiltonian stability of compact minimal Lagrangian submanifolds embedded in complex hyperquadrics which are obtained as Gauss images of isoparametric hypersurfaces in spheres with g(=1,2,3) distinct principal curvatures.