HAMILTONIAN STATIONARY CONES WITH ISOTROPIC LINKS

摘要

We show that any closed oriented immersed Hamiltonian stationary isotropic surface Sigma with genus g(Sigma) in S-5 subset of C-3 is (1) Legendrian and minimal if g(Sigma) = 0; (2) either Legendrian or with exactly 2g(Sigma) -2 Legendrian points if g(Sigma) >= 1. In general, every compact oriented immersed isotropic submanifold Ln-1 subset of S2n-1 subset of C-n such that the cone C(Ln-1) is Hamiltonian stationary must be Legendrian and minimal if its first Betti number is zero. Corresponding results for nonorientable links are also provided.