Ruled lagrangian submanifolds in complex euclidean 3-space

その他

We show that if ruled Lagrangian submanifold M^3 in 3-dimensional complex Euclidean space is Einstein, then it is flat, provided that the map which gives direction of each ruling has constant rank. Also we give explicit construction of flat ruled Lagrangian submanifolds M^3 in C^3, from some horizontal curves in S^5, such that M^3 is neither totally geodesic nor Riemannian product Σ×R.