It is well known that TS^n-1 is diffeomorphic to M= f^{-1}(1) where f:C^n---->C, f=\sum_{i=1}^{n} z_{i}^{2}. two question: 1)Is M a symplectic submanifold of C^n ~ R^2n (with the standard symplectic structure)?

if the answer is affirmative, we can consider two symplectic structure for TS^n-1. The first is the original structure of the tangent or cotangent bundle, the second one is the pull back structure of M

2)are these structures equivalent?