Mathematics – Differential Geometry
Scientific paper
2007-05-05
Mathematics
Differential Geometry
38 pages, v2, minor corrections made
Scientific paper
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.
Ma Hui
Ohnita Yoshihiro
No associations
LandOfFree
On Lagrangian submanifolds in complex hyperquadrics and isoparametric hypersurfaces in spheres does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On Lagrangian submanifolds in complex hyperquadrics and isoparametric hypersurfaces in spheres, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Lagrangian submanifolds in complex hyperquadrics and isoparametric hypersurfaces in spheres will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-28450