On a Minimal Lagrangian Submanifold of Cn Foliated by Spheres

摘要

In general, not much is known about minimal submanifolds of Euclidean space of high codimension. In [l] , Anderson studies complete minimal submanifolds of Euclidean space with finite total scalar curvature, trying to generalize classical re- sults of minimal surfaces. More recently, Moore [10] continues the study of this kind of minimal submanifolds. Harvey and Lawson [6] also study a paticular family of minimal submanifolds of complex Euclidean space, the special Lagrangian submanifolds-that is, ori- ented minimal Lagrangian submanifolds. They have the property of being abso- lutely volume minimizing. Among other things, they construct important exam- ples of the previously mentioned minimal Lagrangian submamfolds.