Lagrangian submanifolds of C~n with conformal Maslov form and the Whitney sphere

摘要

Let C~n be the n-dimensional complex Euclidean space, < , > the Euclidean metric and J the canonical complex structure on C~n. The Kaehler two form Ω is given by Ω(v, w) = < v,Jw > , for any vectors v, w in C~n. We say that an immersion ψ : M → C~n of an n-dimensional manifold M is Lagrangian if ψ~* Ω ≡ 0.